# questions

tags: ['Physics', 'Rotational Motion', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch1_P1.db
title:
a-uniform-solid-cylindrical-roller-of-mass-m-is-being-pulled-on-horizontal-surface-with-force-f-parallel-to-the-surface-applied-at-its-centre-if-the-a

slug:
a-uniform-solid-cylindrical-roller-of-mass-m-is-being-pulled-on-horizontal-surface-with-force-f-parallel-to-the-surface-applied-at-its-centre-if-the-a-47886

question:
<div class="question">A uniform solid cylindrical roller of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> is being pulled on horizontal surface with force <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math> parallel to the surface applied at its centre. If the acceleration of the cylinder is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and it is rolling without slipping, then the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi>m</mi><mi>a</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><mi>m</mi><mi>a</mi></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo> </mo><mi>m</mi><mi>a</mi></mrow><mn>2</mn></mfrac></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mo> </mo><mi>m</mi><mi>a</mi></mrow><mn>2</mn></mfrac></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo> </mo><mi>m</mi><mi>a</mi></mrow><mn>2</mn></mfrac></math></span> </div>

answer:
<div class="solution"><p>By Newton's law of motion</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>-</mo><msub><mi>f</mi><mi>s</mi></msub><mo>=</mo><mi>m</mi><mi>a</mi></math>                   ...(i)</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/05358344-ac1b-4eda-85b0-50c97631bbb1-image.png" style="width: 210px; height: 142px;"/></p><p>and torque, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>τ</mi><mo>=</mo><mi>l</mi><mi>α</mi></math></p><p>where, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mo>=</mo></math> tangential component of acceleration<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mtext> moment of inertia </mtext></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo>  </mo><mi>f</mi><mi>R</mi><mo>=</mo><mi>l</mi><mi>α</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mi>R</mi><mo>=</mo><mfrac><mrow><mi>M</mi><msup><mi>R</mi><mn>2</mn></msup></mrow><mn>2</mn></mfrac><mo>·</mo><mfrac><mi>a</mi><mi>R</mi></mfrac><mfenced close="" open="["><mrow><mo>∴</mo><mi>I</mi><mo>=</mo><mfrac><mrow><mi>M</mi><msup><mi>R</mi><mn>2</mn></msup></mrow><mn>2</mn></mfrac></mrow></mfenced></math>and <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open=""><mrow><mo>,</mo><mi>α</mi><mo>=</mo><mfrac><mi>a</mi><mi>R</mi></mfrac></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo>  </mo><mi>f</mi><mo>=</mo><mfrac><mrow><mi>m</mi><mi>a</mi></mrow><mn>2</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mo> </mo><mi>F</mi><mo>=</mo><mi>f</mi><mo>+</mo><mi>m</mi><mi>a</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mi>m</mi><mi>a</mi></mrow><mn>2</mn></mfrac><mo>+</mo><mi>m</mi><mi>a</mi><mo>=</mo><mfrac><mrow><mn>3</mn><mi>m</mi><mi>a</mi></mrow><mn>2</mn></mfrac></math></p></div>


tags: ['Mathematics', 'Vector Algebra', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch1_P1.db
title:
a-vector-perpendicular-to-the-plane-containing-the-vectors-i-2-j-k-and-3-i-2-j-k-is-inclined-to-the-vector-i-j-k-at-an-angle

slug:
a-vector-perpendicular-to-the-plane-containing-the-vectors-i-2-j-k-and-3-i-2-j-k-is-inclined-to-the-vector-i-j-k-at-an-angle-12401

question:
<div class="question">A vector perpendicular to the plane containing the vectors $\hat{i}-2 \hat{j}-\hat{k}$ and $3 \hat{i}-2 \hat{j}-\hat{k}$ is inclined to the vector $\hat{i}+\hat{j}+\hat{k}$ at an angle</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\tan ^{-1} \sqrt{14}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\sec ^{-1} \sqrt{14}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\tan ^{-1} \sqrt{15}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\tan ^{-1} \sqrt{14}$</span> </div>

answer:
<div class="solution">A vector perpendicular to the plane is<br/>$\begin{aligned}<br/>&amp; (\hat{i}-2 \hat{j}-\hat{k}) \times(3 \hat{i}-2 \hat{j}-\hat{k}) \\<br/>&amp; =\left|\begin{array}{ccc}<br/>\hat{i} &amp; \hat{j} &amp; \hat{k} \\<br/>1 &amp; -2 &amp; -1 \\<br/>3 &amp; -2 &amp; -1<br/>\end{array}\right|=-2 \hat{j}+4 \hat{k} \\<br/>&amp; \Rightarrow \text { unit vector } \hat{a}=\frac{-2 \hat{j}+4 \hat{k}}{\sqrt{4+16}}=\frac{-2 \hat{j}+4 \hat{k}}{2 \sqrt{5}}<br/>\end{aligned}$<br/>Angle between the unit vector and $\vec{r}=\hat{i}+\hat{j}+\hat{k}$<br/>$=\cos ^{-1} \frac{\vec{r} \cdot \hat{a}}{|\vec{r}| \cdot|\hat{a}|}=\cos ^{-1} \frac{1}{\sqrt{15}}=\tan ^{-1} \sqrt{14}$</div>


tags: ['Physics', 'Thermodynamics', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch1_P1.db
title:
a-vessel-containing-1-more-of-o-2-gas-molar-mass-32-at-temperature-t-the-pressure-of-the-gas-is-p-an-identical-vessel-containing-one-mole-of-he-gas-mo

slug:
a-vessel-containing-1-more-of-o-2-gas-molar-mass-32-at-temperature-t-the-pressure-of-the-gas-is-p-an-identical-vessel-containing-one-mole-of-he-gas-mo-87898

question:
<div class="question">A vessel containing 1 more of $\mathrm{O}_{2}$ gas (molar mass  32) at temperature $\mathrm{T}$. The pressure of the gas is p. An identical vessel containing one mole of he gas (molar mass 4 ) at temperature $2 \mathrm{~T}$ has a pressure of</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{p} / 8$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{p}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$2 \mathrm{p}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$8 \mathrm{p}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2 \mathrm{p}$</span> </div>

answer:
<div class="solution">Applying gas equation, $\mathrm{pV}=\mathrm{nRT}$ We can write, $\mathrm{p}_{1} \mathrm{~V}=\mathrm{n}_{1} \mathrm{RT}_{1}$ and $\mathrm{p}_{2} \mathrm{~V}=\mathrm{n}_{2} \mathrm{RT}_{2}$
<br/> <br/>$\Rightarrow \quad \frac{\mathrm{p}_{2}}{\mathrm{p}_{1}}=\frac{\mathrm{n}_{2}}{\mathrm{n}_{1}} \times \frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}=\frac{1}{1} \times \frac{2 \mathrm{~T}}{\mathrm{~T}}=2$
<br/> <br/>$\Rightarrow \mathrm{p}_{2}=2 \mathrm{p}$</div>


tags: ['Physics', 'Ray Optics', 'BITSAT', 'BITSAT 2020']
answer: <div class="solution">Apparent depth $=\mathrm{d} / \mu_{1}+\mathrm{d} / \mu_{2}$</div>
source_db: MarksBatch1_P1.db
title:
a-vessel-of-depth-2-d-cm-is-half-filled-with-a-liquid-of-refractive-index-1-and-the-upper-half-with-a-liquid-of-refractive-index-2-the-apparent-depth-

slug:
a-vessel-of-depth-2-d-cm-is-half-filled-with-a-liquid-of-refractive-index-1-and-the-upper-half-with-a-liquid-of-refractive-index-2-the-apparent-depth-38076

question:
<div class="question">A vessel of depth $2 \mathrm{~d} \mathrm{~cm}$ is half filled with a liquid of refractive index $\mu_{1}$ and the upper half with a liquid of refractive index $\mu_{2}$. The apparent depth of the vessel seen perpendicularly is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\left(\frac{\mu_{1} \mu_{2}}{\mu_{1}+\mu_{2}}\right) \mathrm{d}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\left(\frac{1}{\mu_{1}}+\frac{1}{\mu_{2}}\right) \mathrm{d}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left(\frac{1}{\mu_{1}}+\frac{1}{\mu_{2}}\right) 2 \mathrm{~d}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\left(\frac{1}{\mu_{1} \mu_{2}}\right) 2 \mathrm{~d}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(\frac{1}{\mu_{1}}+\frac{1}{\mu_{2}}\right) \mathrm{d}$</span> </div>


tags: ['Physics', 'Ray Optics', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch1_P1.db
title:
a-vessel-of-depth-2-d-cm-is-halffilled-with-a-liquid-of-refractive-index-1-and-the-upper-half-with-a-liquid-of-refractive-index-2-the-apparent-depth-o

slug:
a-vessel-of-depth-2-d-cm-is-halffilled-with-a-liquid-of-refractive-index-1-and-the-upper-half-with-a-liquid-of-refractive-index-2-the-apparent-depth-o-34979

question:
<div class="question">A vessel of depth $2 \mathrm{~d} \mathrm{~cm}$. is halffilled with a liquid of refractive index $\mu_{1}$ and the upper half with a liquid of refractive index $\mu_{2} .$ The apparent depth of the vessel seen perpendicularly is -</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$d\left(\frac{\mu_{1} \mu_{2}}{\mu_{1}+\mu_{2}}\right)$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$d\left(\frac{1}{\mu_{1}}+\frac{1}{\mu_{2}}\right)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2 d\left(\frac{1}{\mu_{1}}+\frac{1}{\mu_{2}}\right)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 d\left(\frac{1}{\mu_{1} \mu_{2}}\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$d\left(\frac{1}{\mu_{1}}+\frac{1}{\mu_{2}}\right)$</span> </div>

answer:
<div class="solution">$\mathrm{h}^{\prime}=\frac{\mathrm{d}_{1}}{\mu_{1}}+\frac{\mathrm{d}_{2}}{\mu_{2}}=\mathrm{d}\left(\frac{1}{\mu_{1}}+\frac{1}{\mu_{2}}\right)$</div>


tags: ['Physics', 'Thermodynamics', 'BITSAT', 'BITSAT 2015']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2: 5</span> </div>
source_db: MarksBatch1_P1.db
title:
a-vessel-of-volume-20l-contains-a-mixture-of-hydrogen-and-helium-at-temperature-of-2-7-c-and-pressure-2-atm-the-mass-of-mixture-is-5-g-assuming-the-ga

slug:
a-vessel-of-volume-20l-contains-a-mixture-of-hydrogen-and-helium-at-temperature-of-2-7-c-and-pressure-2-atm-the-mass-of-mixture-is-5-g-assuming-the-ga-54656

question:
<div class="question">A vessel of volume 20L contains a mixture of hydrogen and helium at temperature of $27^{\circ} \mathrm{C}$ and pressure 2 atm. The mass of mixture is $5 \mathrm{~g}$. Assuming the gases to be ideal, the ratio of mass of hydrogen to that of helium in the given mixture will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1: 2</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2: 3</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2: 1</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">2: 5</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">Let there are $\mathrm{n}_{1}$ moles of hydrogen and $\mathrm{n}_{2}$ moles of helium in the given mixture. As $\mathrm{Pv}$ $=\mathrm{nRT}$
<br/> <br/>Then the pressure of the mixture
<br/> <br/>$$
<br/> <br/>\begin{array}{r}
<br/> <br/>P=\frac{\mathrm{n}_{1} \mathrm{RT}}{\mathrm{V}}+\frac{\mathrm{n}_{2} \mathrm{RT}}{\mathrm{V}}=\left(\mathrm{n}_{1}+\mathrm{n}_{2}\right) \frac{\mathrm{RT}}{\mathrm{V}} \\
<br/> <br/>2 \times 101.3 \times 10^{3}=\left(\mathrm{n}_{1}+\mathrm{n}_{2}\right) \times \frac{(8.3 \times 300)}{20 \times 10^{-3}}
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>or,
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\left(\mathrm{n}_{1}+\mathrm{n}_{2}\right)=\frac{2 \times 101.3 \times 10^{3} \times 20 \times 10^{-3}}{(8.3)(300)} \\
<br/> <br/>\text { or, } \mathrm{n}_{1}+\mathrm{n}_{2}=1.62
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>The mass of the mixture is (in grams)
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\mathrm{n}_{1} \times 2+\mathrm{n}_{2} \times 4=5 \\
<br/> <br/>\Rightarrow \quad\left(\mathrm{n}_{1}+2 \mathrm{n}_{2}\right)=2.5 \quad \ldots
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>Solving the eqns. (1) and (2), we get $\mathrm{n}_{1}=0.74$ and $\mathrm{n}_{2}=0.88$
<br/> <br/>Hence, $\frac{\mathrm{m}_{\mathrm{H}}}{\mathrm{m}_{\mathrm{He}}}=\frac{0.74 \times 2}{0.88 \times 4}=\frac{1.48}{3.52}=\frac{2}{5}$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P1.db
title:
a-vessel-with-water-is-placed-on-a-weighing-pan-and-it-reads-600-g-now-a-ball-of-mass-40-g-and-density-080-g-cm-3-is-sunk-into-the-water-with-a-pin-of

slug:
a-vessel-with-water-is-placed-on-a-weighing-pan-and-it-reads-600-g-now-a-ball-of-mass-40-g-and-density-080-g-cm-3-is-sunk-into-the-water-with-a-pin-of-82423

question:
<div class="question">A vessel with water is placed on a weighing pan and it reads $600 \mathrm{~g}$. Now a ball of mass $40 \mathrm{~g}$ and density $0.80 \mathrm{~g} \mathrm{~cm}^{-3}$ is sunk into the water with a pin of negligible volume, as shown in figure keeping it sunk. The weighing pan will show a reading
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/rW9r6DaQvSqwpKV8WmWHLHNt3EVSO226-d7Su_nRK8k.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$600 \mathrm{~g}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$550 \mathrm{~g}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$650 \mathrm{~g}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$632 \mathrm{~g}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$650 \mathrm{~g}$</span> </div>

answer:
<div class="solution">Volume of ball $=\frac{40}{0.8}=50 \mathrm{~cm}^{3}$
<br/> <br/>Downthrust on water $=50 \mathrm{~g}$. Therefore reading is $650 \mathrm{~g}$.</div>


tags: ['Physics', 'Waves and Sound', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch1_P1.db
title:
a-wave-y-a-sin-t-k-x-on-a-string-meets-with-another-wave-producing-a-node-at-x-0-then-the-equation-of-the-unknown-wave-is-1

slug:
a-wave-y-a-sin-t-k-x-on-a-string-meets-with-another-wave-producing-a-node-at-x-0-then-the-equation-of-the-unknown-wave-is-1-77708

question:
<div class="question">A wave $y=a \sin (\omega t-k x)$ on a string meets with another wave producing a node at $\mathrm{x}=0 .$ Then the equation of the unknown wave is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$y=a \sin (\omega t+k x)$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$y=-a \sin (\omega t+k x)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$y=a \sin (\omega t-k x)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$y=-a \sin (\omega t-k x)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$y=-a \sin (\omega t+k x)$</span> </div>

answer:
<div class="solution">Equation of a wave $y_{1}=a \sin (\omega t-k x)$....(i)<br/>Let equations of another wave may be, $y_{2}=a \sin (\omega t+k x)$....(ii)<br/>$y_{3}=-a \sin (\omega t+k x) \quad \ldots .$ (iii)<br/>If Eq. (i) propagate with Eq. (ii), we get $\mathrm{y}=2 \mathrm{a} \cos \mathrm{kx} \sin \omega \mathrm{t}$<br/>If Eq. (i), propagate with Eq. (iii), we get $y=-2 a \sin k x \cos \omega t$<br/>At $x=0, y=0,$ wave produce node <br/>So, Eq.(iii) is the equation of unknown wave</div>


tags: ['Physics', 'Motion In Two Dimensions', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P1.db
title:
a-wheel-is-rotating-at-900-r-pm-about-its-axis-when-power-is-cut-offit-comes-to-rest-in-1-minute-the-angular-retardation-in-rad-s-2-is

slug:
a-wheel-is-rotating-at-900-r-pm-about-its-axis-when-power-is-cut-offit-comes-to-rest-in-1-minute-the-angular-retardation-in-rad-s-2-is-54593

question:
<div class="question">A wheel is rotating at $900 \mathrm{r}$.p.m. about its axis. When power is cut offit comes to rest in 1 minute. The angular retardation in $\mathrm{rad} / \mathrm{s}^{2}$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\pi / 2$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\pi / 4$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\pi / 6$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\pi / 8$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\pi / 2$</span> </div>

answer:
<div class="solution">Angular retardation,
<br/> <br/>$\begin{aligned} \alpha &amp;=\frac{\omega_{2}-\omega_{1}}{t}=\frac{2 \pi\left(\mathrm{n}_{2}-\mathrm{n}_{1}\right)}{\mathrm{t}} \\ &amp;=\frac{2 \pi(0-900 / 60)}{60}=\frac{\pi}{2} \mathrm{rad} / \mathrm{s}^{2} \end{aligned}$</div>


tags: ['Physics', 'Motion In Two Dimensions', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch1_P1.db
title:
a-wheel-of-radius-r-rolls-on-the-ground-with-a-uniform-velocity-v-the-relative-acceleration-of-topmost-point-of-the-wheel-with-respect-to-the-bottom-m

slug:
a-wheel-of-radius-r-rolls-on-the-ground-with-a-uniform-velocity-v-the-relative-acceleration-of-topmost-point-of-the-wheel-with-respect-to-the-bottom-m-40235

question:
<div class="question">A wheel of radius $\mathrm{R}$ rolls on the ground with a uniform velocity $\mathrm{v}$. The relative acceleration of topmost point of the wheel with respect to the bottom most point is
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/onXV_CBaeBCQKk1QE6yt9n2V7mRxvHV2Dara3e1cO9c.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\mathrm{v}^{2}}{\mathrm{R}}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{2 \mathrm{v}^{2}}{\mathrm{R}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\mathrm{v}^{2}}{2 \mathrm{R}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{4 \mathrm{v}^{2}}{\mathrm{R}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{2 \mathrm{v}^{2}}{\mathrm{R}}$</span> </div>

answer:
<div class="solution">As $a_{\mathrm{CM}}=0 \quad\left[\mathrm{v}_{\mathrm{CM}}=\right.$ constant $]$, Tangential acceleration of each point $\left|\overrightarrow{\mathrm{a}}_{\mathrm{AB}}\right|=\frac{2 \mathrm{v}^{2}}{\mathrm{R}}$</div>


tags: ['Physics', 'Waves and Sound', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P1.db
title:
a-whistle-of-frequency-500-hz-tied-to-the-end-of-a-string-of-length-1-2-m-revolves-at-400-rev-min-1-a-listener-standing-some-distance-away-in-the-plan

slug:
a-whistle-of-frequency-500-hz-tied-to-the-end-of-a-string-of-length-1-2-m-revolves-at-400-rev-min-1-a-listener-standing-some-distance-away-in-the-plan-55176

question:
<div class="question">A whistle of frequency <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mi>Hz</mi></math> tied to the end of a string of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>2</mn><mo> </mo><mi mathvariant="normal">m</mi></math> revolves at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>400</mn><mo> </mo><mi>rev</mi><mo> </mo><msup><mi>min</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>. A listener standing some distance away in the plane of rotation of whistle hears frequencies in the range. (Speed of sound <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>340</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>436</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>574</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>426</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>586</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>426</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>574</mn></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>436</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>586</mn></math></p></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>436</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>586</mn></math></p></span> </div>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>s</mi></msub><mo>=</mo><mi>r</mi><mi>ω</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><mn>2</mn><mi>π</mi><mi>f</mi></math>   <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>∵</mo><mi>ω</mi><mo>=</mo><mn>2</mn><mi>π</mi><mi>f</mi></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><mn>2</mn><mo>×</mo><mn>3</mn><mo>.</mo><mn>14</mn><mo>×</mo><mfenced><mfrac><mn>400</mn><mn>60</mn></mfrac></mfenced><mo>=</mo><mn>50</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>min</mi></msub><mo>=</mo><mfrac><mi>v</mi><mrow><mi>v</mi><mo>+</mo><msub><mi>v</mi><mi>s</mi></msub></mrow></mfrac><mo>·</mo><mi>v</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>340</mn><mrow><mn>340</mn><mo>+</mo><mn>50</mn></mrow></mfrac><mo>×</mo><mn>500</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>436</mn><mo> </mo><mi>Hz</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>max</mi></msub><mo>=</mo><mfrac><mi>v</mi><mrow><mi>v</mi><mo>-</mo><msub><mi>v</mi><mi>s</mi></msub></mrow></mfrac><mo>·</mo><mi>v</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>340</mn><mrow><mn>340</mn><mo>-</mo><mn>50</mn></mrow></mfrac><mo>×</mo><mn>500</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>586</mn><mo> </mo><mi>Hz</mi></math></p></div>


tags: ['Physics', 'Waves and Sound', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P1.db
title:
a-whistle-of-frequency-1000-hz-is-sounded-on-a-car-travelling-towards-a-cliff-with-velocity-of-18-m-s-1-normal-to-the-cliff-if-c-330-m-s-1-then-the-ap

slug:
a-whistle-of-frequency-1000-hz-is-sounded-on-a-car-travelling-towards-a-cliff-with-velocity-of-18-m-s-1-normal-to-the-cliff-if-c-330-m-s-1-then-the-ap-50168

question:
<div class="question">A whistle of frequency $1000 \mathrm{~Hz}$ is sounded on a car travelling towards a cliff with velocity of 18 $\mathrm{~m} \mathrm{~s}^{-1}$ normal to the cliff. If $\mathrm{c}=330 \mathrm{~m} \mathrm{~s}^{-1}$, then the apparent frequency of the echo as heard by the car driver is nearly</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$1115 \mathrm{~Hz}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$115 \mathrm{~Hz}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$67 \mathrm{~Hz}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$47.2 \mathrm{~Hz}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1115 \mathrm{~Hz}$</span> </div>

answer:
<div class="solution">By the concept of accoustic, the observer and source are moving towards each other, each with a velocity of $18 \mathrm{~m} \mathrm{~s}^{-1}$ $\therefore \mathrm{v}^{\prime}=\frac{330+18}{330-18} \times 1000 \approx 1115 \mathrm{~Hz}$</div>


tags: ['Mathematics', 'Sequences and Series', 'BITSAT', 'BITSAT 2010']
answer: <div class="solution">For maximum profit, \(z=40 x+25 y\).</div>
source_db: MarksBatch1_P1.db
title:
a-wholesale-merchant-wants-to-start-the-business-of-cereal-with-24000-wheat-is-400-per-quintal-and-rice-is-600-per-quintal-he-has-capacity-to-store-20

slug:
a-wholesale-merchant-wants-to-start-the-business-of-cereal-with-24000-wheat-is-400-per-quintal-and-rice-is-600-per-quintal-he-has-capacity-to-store-20-66424

question:
<div class="question">A wholesale merchant wants to start the business of cereal with \(â¹ 24000\). Wheat is \(â¹ 400\) per quintal and rice is \(â¹ 600\) per quintal. He has capacity to store 200 quintal cereal. He earns the profit \(â¹ 25\) per quintal on wheat and â¹ 40 per quintal on rice. If he store \(\mathrm{x}\) quintal rice and y quintal wheat, then for maximum profit the objective function is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(25 x+40 y\)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\(40 x+25 y\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(400 \mathrm{x}+600 \mathrm{y}\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(\frac{400}{40} \mathrm{x}+\frac{600}{25} \mathrm{y}\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(40 x+25 y\)</span> </div>


tags: ['Mathematics', 'Area Under Curves', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch1_P1.db
title:
a-wire-34-cm-long-is-to-be-bent-in-the-form-of-a-quadrilateral-of-which-each-angle-is-9-0-what-is-the-maximum-area-which-can-be-enclosed-inside-the-qu-1

slug:
a-wire-34-cm-long-is-to-be-bent-in-the-form-of-a-quadrilateral-of-which-each-angle-is-9-0-what-is-the-maximum-area-which-can-be-enclosed-inside-the-qu-1-89335

question:
<div class="question">A wire $34 \mathrm{~cm}$ long is to be bent in the form of a quadrilateral of which each angle is $90^{\circ} .$ What is the maximum area which can be enclosed inside the quadrilateral?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$68 \mathrm{~cm}^{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$70 \mathrm{~cm}^{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$71.25 \mathrm{~cm}^{2}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$72.25 \mathrm{~cm}^{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$72.25 \mathrm{~cm}^{2}$</span> </div>

answer:
<div class="solution">Let one side of quadrilateral be $\mathrm{x}$ and another side be $y$ so, $2(x+y)=34$
<br/> <br/>or $(x+y)=17$
<br/> <br/>We know from the basic principle that for a given perimeter square has the maximum area, $\mathrm{so}, \mathrm{x}=\mathrm{y}$ and putting this value in equation (i)
<br/> <br/>$\mathrm{x}=\mathrm{y}=\frac{17}{2}$
<br/> <br/>Area $=x \cdot y=\frac{17}{2} \times \frac{17}{2}=\frac{289}{4}=72.25$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2016']
answer: <div class="solution">No Solution</div>
source_db: MarksBatch1_P1.db
title:
a-wire-carrying-current-i-has-the-shape-as-shown-in-adjoining-figure-linear-parts-of-the-wire-are-very-long-and-parallel-to-x-axis-while-semicircular-

slug:
a-wire-carrying-current-i-has-the-shape-as-shown-in-adjoining-figure-linear-parts-of-the-wire-are-very-long-and-parallel-to-x-axis-while-semicircular-99504

question:
<div class="question">A wire carrying current I has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to $\mathrm{X}$ -axis while semicircular portion of radius $\mathrm{R}$ is lying in Y-Z plane. Magnetic field at point $\mathrm{O}$ is:
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/OzqsbqXH-pIhPt6PG4ouMptSG7rgSQn0VWN8j4HaaxM.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\overrightarrow{\mathrm{B}}=-\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\mu \hat{\mathrm{i}} \times 2 \hat{\mathrm{k}})$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\quad \overrightarrow{\mathrm{B}}=-\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\pi \hat{\mathrm{i}}+2 \hat{\mathrm{k}})$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\overrightarrow{\mathrm{B}}=\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\pi \hat{\mathrm{i}}-2 \hat{\mathrm{k}})$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\overrightarrow{\mathrm{B}}=\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\pi \hat{\mathrm{i}}+2 \hat{\mathrm{k}})$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad \overrightarrow{\mathrm{B}}=-\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\pi \hat{\mathrm{i}}+2 \hat{\mathrm{k}})$</span> </div>


tags: ['Physics', 'Current Electricity', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P1.db
title:
a-wire-of-a-certain-material-is-stretched-slowly-by-ten-per-cent-its-new-resistance-and-specific-resistance-become-respectively

slug:
a-wire-of-a-certain-material-is-stretched-slowly-by-ten-per-cent-its-new-resistance-and-specific-resistance-become-respectively-87048

question:
<div class="question">A wire of a certain material is stretched slowly by ten per cent. Its new resistance and specific resistance become respectively:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1.2$ times, $1.3$ times</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$1.21$ times, same</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">both remain the same</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1.1$ times, $1.1$ times</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1.21$ times, same</span> </div>

answer:
<div class="solution">\(\mathrm{R}=\frac{\rho \mathrm{l}}{\mathrm{A}}\)
<br/> <br/>Now, \(1=1+\frac{1}{10}=\frac{111}{10}\)
<br/> <br/>and therefore, \(\mathrm{A}=\frac{10 \mathrm{~A}}{11}\)
<br/> <br/>So \(\mathrm{R}^{\prime}=\frac{\mathrm{p} \times\left(\frac{111}{10}\right)}{\frac{10 \mathrm{~A}}{11}}=\frac{\rho \mathrm{l}}{\mathrm{A}} \times \frac{(11)^{2}}{(10)^{2}}=1.21 \mathrm{R}\)
<br/> <br/>Now resistance becomes \(1.21\) times of initial and specific resistance is the intrinsic property so remains same.</div>


tags: ['Physics', 'Current Electricity', 'BITSAT', 'BITSAT 2014']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2: 1</span> </div>
source_db: MarksBatch1_P1.db
title:
a-wire-x-is-half-the-diameter-and-half-the-length-of-a-wire-y-of-similar-material-the-ratio-of-resistance-of-x-to-that-of-y-is

slug:
a-wire-x-is-half-the-diameter-and-half-the-length-of-a-wire-y-of-similar-material-the-ratio-of-resistance-of-x-to-that-of-y-is-52575

question:
<div class="question">A wire $X$ is half the diameter and half the length of a wire $Y$ of similar material. The ratio of resistance of $\mathrm{X}$ to that of $\mathrm{Y}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">8: 1</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">4: 1</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">2: 1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">1: 1</span> </li> </ul>

answer:
<div class="solution">$\mathrm{R} \propto \frac{\ell}{\mathrm{D}^{2}} \Rightarrow \frac{\mathrm{Rx}}{\mathrm{Ry}}=\frac{2}{1}$</div>


tags: ['Physics', 'Semiconductors', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P1.db
title:
a-zener-diode-of-voltage-v-z-6-v-is-used-to-maintain-a-constant-voltage-across-a-load-resistance-r-l-1000-by-using-a-series-resistance-r-s-100-if-the-

slug:
a-zener-diode-of-voltage-v-z-6-v-is-used-to-maintain-a-constant-voltage-across-a-load-resistance-r-l-1000-by-using-a-series-resistance-r-s-100-if-the-51035

question:
<div class="question">A zener diode of voltage $\mathrm{V}_{\mathrm{Z}}(=6 \mathrm{~V})$ is used to maintain a constant voltage across a load resistance $\mathrm{R}_{\mathrm{L}}(=1000 \Omega)$ by using a series resistance $R_{\mathrm{s}}(=100 \Omega)$. If the e.m.f. of source is $\mathrm{E}(=9 \mathrm{~V})$, what is the power being dissipated in Zener diode?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$0.144$ watt</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.324$ watt</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0.244$ watt</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0.544$ watt</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.144$ watt</span> </div>

answer:
<div class="solution">Here, $E=9 \mathrm{~V} ; \mathrm{V}_{\mathrm{z}}=6 ; \mathrm{R}_{\mathrm{L}}=1000 \Omega$ and $\mathrm{R}_{\mathrm{s}}=100 \Omega$,
<br/> <br/>Potential drop across series resistor $\mathrm{V}=\mathrm{E}-\mathrm{V}_{\mathrm{Z}}=9-6=3 \mathrm{~V}$
<br/> <br/>Current through series resistance $R_{S}$ is $\mathrm{I}=\frac{\mathrm{V}}{\mathrm{R}}=\frac{3}{100}=0.03 \mathrm{~A}$
<br/> <br/>Current through load resistance $R_{L}$ is $\mathrm{I}_{\mathrm{L}}=\frac{\mathrm{V}_{\mathrm{Z}}}{\mathrm{R}_{\mathrm{L}}}=\frac{6}{1000}=0.006 \mathrm{~A}$
<br/> <br/>Current through Zener diode is $\mathrm{I}_{\mathrm{Z}}=\mathrm{I}-\mathrm{I}_{\mathrm{L}}=0.03-0.006=0.024 \mathrm{amp} .$ Power dissipated in Zener diode is $\mathrm{P}_{\mathrm{Z}}=\mathrm{V}_{\mathrm{Z}} \mathrm{I}_{\mathrm{Z}}=6 \times 0.024=0.144 \mathrm{Watt}$</div>


tags: ['Mathematics', 'Heights and Distances', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P1.db
title:
abc-is-a-triangular-park-with-ab-ac-100-m-a-tv-tower-stands-at-the-midpoint-of-bc-the-angles-of-elevation-of-the-top-of-the-tower-at-a-b-c-are-4-5-6-0

slug:
abc-is-a-triangular-park-with-ab-ac-100-m-a-tv-tower-stands-at-the-midpoint-of-bc-the-angles-of-elevation-of-the-top-of-the-tower-at-a-b-c-are-4-5-6-0-68308

question:
<div class="question">$\mathrm{ABC}$ is a triangular park with $\mathrm{AB}=\mathrm{AC}=100 \mathrm{~m} . \mathrm{A}$ TV tower stands at the mid-point of $\mathrm{BC}$. The angles of elevation of the top of the tower at A, B, C are $45^{\circ}, 60^{\circ}, 60^{\circ}$ respectively. The height of the tower is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$50 \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$50 \sqrt{3} \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$50 \sqrt{2} \mathrm{~m}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$50(3-\sqrt{3}) \mathrm{m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$50 \sqrt{3} \mathrm{~m}$</span> </div>

answer:
<div class="solution">$\tan 45^{\circ}=\frac{\mathrm{PQ}}{\mathrm{AQ}}=\frac{\mathrm{h}}{\mathrm{AQ}} \Rightarrow \mathrm{h}=\mathrm{AQ}$
<br/> <br/>Where $\mathrm{PQ}$ is tower and $\mathrm{ABC}$ is the park, with $\mathrm{Q}$ being mid point of the side $\mathrm{BC}$ and $\mathrm{PQ}=\mathrm{h}$ Also, $A Q^{2}+B Q^{2}=100^{2}$
<br/> <br/>$\Rightarrow \mathrm{h}^{2}+\mathrm{h}^{2} \cot ^{2} 60^{\circ}=100^{2}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/tuAM6FNFOsmKk75aDThfd9hkBNGpcAj1vMCBk-QdOjY.original.fullsize.png"/><br/> <br/> <br/>$\Rightarrow \mathrm{h}^{2}\left[1+\frac{1}{3}\right]=100^{2}$
<br/> <br/>$\Rightarrow \mathrm{h}^{2}=\frac{3 \times 100^{2}}{4} \Rightarrow \mathrm{h}=50 \sqrt{3}$</div>


title: according-to-iupac-system-the-correct-name-of-the-compound-having-the-formula
slug: according-to-iupac-system-the-correct-name-of-the-compound-having-the-formula-35146
tags: ['Chemistry', 'General Organic Chemistry', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch1_P1.db
question:
<div class="question">According to IUPAC system, the correct name of the compound having the formula<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/29cmiCLRu8UdYCTE-tLStfUOdzmirGUm5or-8InRi0M.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2 -ethyl-3-methyl but- 1 -ene</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2 -methyl pent- 3 -ene</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2 -methyl but- 1 -ene</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">None of these</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">None of these</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/sGhbzLvJyK1n7buDUQR0MYRqBmLPcvOiDw9YiMYCLK8.original.fullsize.png"/></div>


title: acetaldehyde-and-acetone-can-be-distinguished-by
slug: acetaldehyde-and-acetone-can-be-distinguished-by-61278
question: <div class="question">Acetaldehyde and acetone can be distinguished by :</div>
tags: ['Chemistry', 'Aldehydes and Ketones', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Iodoform test</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Nitroprusside test</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Fehlings solution test</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$C$ \&amp; P test</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Fehlings solution test</span> </div>

answer:
<div class="solution">Acetaldehyde is easily oxidised to acetic acid by a mild oxidising agent like Fehling solution. Acetone is not easily oxidised. Both acetone and acetaldehyde give iodoform test. Other two conditions are not relevant to aldehydes and ketones.</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
acyclicprocess-abcd-is-shown-in-pv-diagram-for-an-ideal-gas-which-of-the-following-diagram-represents-the-same-process-1

slug:
acyclicprocess-abcd-is-shown-in-pv-diagram-for-an-ideal-gas-which-of-the-following-diagram-represents-the-same-process-1-62028

question:
<div class="question">Acyclicprocess ABCD is shown in P-V diagram for an ideal gas. Which of the following diagram represents the same process?
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/Io-ECzOyZ8Mm11B5M1o-EN9YogdjX7drMMTegfwXna4.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ufgIRqkqvYWp6MHKqSBWCZsRot5KsMfFIrBU4qItnCg.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/TBXDMwDKS0B6ay7uFQZ3aj6kgPoedwdcNfQIMpc84_8.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/KgORLGc83p7mbv7B0RjewhNmnQY76aU2H5bsLrYEUgw.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/sSvtephfcStXCy1sxGZuGycChz7RM96W095eBLY4-78.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/KgORLGc83p7mbv7B0RjewhNmnQY76aU2H5bsLrYEUgw.original.fullsize.png"/></span> </div>

answer:
<div class="solution">$\mathrm{AB}$ : Isobaric expansion 
<br/> <br/>$\mathrm{BC}:$ Isothermal expansion
<br/> <br/>CD : Isochoric
<br/> <br/>DA: Isothermal compression</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P1.db
title:
acyclicprocess-abcd-is-shown-in-pv-diagram-for-an-ideal-gas-which-of-the-following-diagram-represents-the-same-process

slug:
acyclicprocess-abcd-is-shown-in-pv-diagram-for-an-ideal-gas-which-of-the-following-diagram-represents-the-same-process-44680

question:
<div class="question">Acyclicprocess ABCD is shown in P-V diagram for an ideal gas. Which of the following diagram represents the same process?
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/Io-ECzOyZ8Mm11B5M1o-EN9YogdjX7drMMTegfwXna4.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ufgIRqkqvYWp6MHKqSBWCZsRot5KsMfFIrBU4qItnCg.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/TBXDMwDKS0B6ay7uFQZ3aj6kgPoedwdcNfQIMpc84_8.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/KgORLGc83p7mbv7B0RjewhNmnQY76aU2H5bsLrYEUgw.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/sSvtephfcStXCy1sxGZuGycChz7RM96W095eBLY4-78.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/KgORLGc83p7mbv7B0RjewhNmnQY76aU2H5bsLrYEUgw.original.fullsize.png"/></span> </div>

answer:
<div class="solution">$\mathrm{AB}$ : Isobaric expansion 
<br/> <br/>$\mathrm{BC}:$ Isothermal expansion
<br/> <br/>CD : Isochoric
<br/> <br/>DA: Isothermal compression</div>


tags: ['Chemistry', 'Surface Chemistry', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P1.db
title:
adsorption-of-a-gas-follows-freundlich-adsorption-isotherm-x-is-the-mass-of-the-gas-adsorbed-on-mass-m-of-the-adsorbent-the-plot-of-m-x-versus-lo-g-p-

slug:
adsorption-of-a-gas-follows-freundlich-adsorption-isotherm-x-is-the-mass-of-the-gas-adsorbed-on-mass-m-of-the-adsorbent-the-plot-of-m-x-versus-lo-g-p-97606

question:
<div class="question">Adsorption of a gas follows Freundlich adsorption isotherm. $x$ is the mass of the gas adsorbed on mass $m$ of the adsorbent. The plot of $\frac{x}{m}$ versus $\log p$ is shown in the given graph.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ZhUCvdIYQVA6OhsEZtwkp47cgQrhbfXqZ9TzF793gCw.original.fullsize.png"/><br/> <br/> <br/>$\frac{x}{m}$ is proportional to :</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$p^{2 / 3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$p^{3 / 2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$p^{3}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$p^{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$p^{2 / 3}$</span> </div>

answer:
<div class="solution">According to Freundlich adsorption isotherm $\frac{x}{m} \propto p^{\frac{1}{n}}, \frac{x}{m}=k p^{\frac{1}{n}}$
<br/> <br/>Slope $=\frac{2}{3}$
<br/> <br/>$\log \frac{x}{m}=\log k+\frac{1}{n} \log p$
<br/> <br/>Slope $=\frac{1}{n}=\frac{2}{3}$
<br/> <br/>$\frac{x}{m} \propto p^{\frac{2}{3}}$</div>


tags: ['Chemistry', 'Solid State', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch1_P1.db
title:
al-at-wt-27-crystallizes-in-the-cubic-system-with-a-cell-edge-of-405-a-its-density-is-27-g-per-cm-3-determine-the-unit-cell-type-calculate-the-radius-

slug:
al-at-wt-27-crystallizes-in-the-cubic-system-with-a-cell-edge-of-405-a-its-density-is-27-g-per-cm-3-determine-the-unit-cell-type-calculate-the-radius-72015

question:
<div class="question">$\mathrm{Al}$ (at. wt 27 ) crystallizes in the cubic system with a cell edge of $4.05 Ãâ¦$. Its density is $2.7 \mathrm{~g}$ per $\mathrm{cm}^{3}$. Determine the unit cell type calculate the radius of the $\mathrm{Al}$ atom</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{fcc}, 2.432 Ã$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">bcc, $2.432 Ã$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">bcc, $1.432 Ã$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{fcc}, 1.432 Ã$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{fcc}, 1.432 Ã$</span> </div>

answer:
<div class="solution">$\rho=\frac{Z \times M}{N_{0} \times a^{3}}$,
<br/> <br/>$$
<br/> <br/>2.7=\frac{Z \times 27}{6.02 \times 10^{23} \times(4.05)^{3} \times 10^{-24}}
<br/> <br/>$$
<br/> <br/>$\therefore Z=4$
<br/> <br/>Hence it is face centred cubic unit lattice.
<br/> <br/>Again $4 r=a \sqrt{2}=5.727 Ãâ¦$
<br/> <br/>$\therefore \mathrm{r}=1.432 Ãâ¦$</div>


title: alizarin-is-an-example-of-1
slug: alizarin-is-an-example-of-1-60977
question: <div class="question">Alizarin is an example of</div>
tags: ['Chemistry', 'Polymers', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Triayl dye</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Azo dye</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Vat dye</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Anthraquinone dye</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Anthraquinone dye</span> </div>

answer:
<div class="solution">Alizarin is an anthraquinone dye. It gives a bright red colour with aluminium and a blue colour with barium.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/KRN7SLha5L4srnb_p4cmaPCGGpZWYppuIJyN4gA-0p0.original.fullsize.png"/></div>


tags: ['Mathematics', 'Permutation Combination', 'BITSAT', 'BITSAT 2016']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">74</span> </div>
source_db: MarksBatch1_P1.db
title:
all-the-words-that-can-be-formed-using-alphabets-a-h-l-u-and-r-are-written-as-in-a-dictionary-no-alphabet-is-repeated-rank-of-the-word-rahul-is

slug:
all-the-words-that-can-be-formed-using-alphabets-a-h-l-u-and-r-are-written-as-in-a-dictionary-no-alphabet-is-repeated-rank-of-the-word-rahul-is-95906

question:
<div class="question">All the words that can be formed using alphabets A, $H, L, U$ and $R$ are written as in a dictionary (no alphabet is repeated). Rank of the word RAHUL is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">71</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">72</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">73</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">74</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">No. of words starting with $\mathrm{A}$ are $4 !=24$
<br/> <br/>No. of words starting with $\mathrm{H}$ are $4 !=24$
<br/> <br/>No. of words starting with $L$ are $4 !=24$
<br/> <br/>These account for 72 words Next word is RAHLU and the $74^{\text {th }}$ word RAHUL</div>


tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch1_P1.db
title:
ammonia-forms-the-complex-ion-cu-nh-3-4-2-with-copper-ions-in-alkaline-solutions-but-not-in-acidic-solutions-what-is-the-reason-for-it-1

slug:
ammonia-forms-the-complex-ion-cu-nh-3-4-2-with-copper-ions-in-alkaline-solutions-but-not-in-acidic-solutions-what-is-the-reason-for-it-1-11397

question:
<div class="question">Ammonia forms the complex ion $\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}$ with copper ions in alkaline solutions but not in acidic solutions. What is the reason for it?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">In acidic solutions protons coordinate with ammonia molecules forming $\mathrm{NH}_{4}^{+}$ ions and $\mathrm{NH}_{3}$ molecules are not available.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">In alkaline solutions insoluble $\mathrm{Cu}(\mathrm{OH})_{2}$ is precipitated which is soluble in excess of any alkali.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Copper hydroxide is an amphoteric substance.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">In acidic solutions hydration protects copper ions.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">In acidic solutions protons coordinate with ammonia molecules forming $\mathrm{NH}_{4}^{+}$ ions and $\mathrm{NH}_{3}$ molecules are not available.</span> </div>

answer:
<div class="solution">$\quad \mathrm{N} \mathrm{H}_{3}+\mathrm{H}^{+}$ (acidic medium) $\rightleftharpoons \mathrm{NH}_{4}^{+}$</div>


title: among-al-2-o-3-sio-2-p-2-o-3-and-so-2-the-correct-order-of-acid-strength-is-1
slug: among-al-2-o-3-sio-2-p-2-o-3-and-so-2-the-correct-order-of-acid-strength-is-1-69480
tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch1_P1.db
question:
<div class="question">Among $\mathrm{Al}_{2} \mathrm{O}_{3}, \mathrm{SiO}_{2}, \mathrm{P}_{2} \mathrm{O}_{3}$ and $\mathrm{SO}_{2}$, the correct<br/>order of acid strength is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{Al}_{2} \mathrm{O}_{3}&lt;\mathrm{SiO}_{2}&lt;\mathrm{SO}_{2}&lt;\mathrm{P}_{2} \mathrm{O}_{3}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{SiO}_{2}&lt;\mathrm{SO}_{2}&lt;\mathrm{Al}_{2} \mathrm{O}_{3}&lt;\mathrm{P}_{2} \mathrm{O}_{3}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{SO}_{2}&lt;\mathrm{P}_{2} \mathrm{O}_{3}&lt;\mathrm{SiO}_{2}&lt;\mathrm{Al}_{2} \mathrm{O}_{3}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{Al}_{2} \mathrm{O}_{3}&lt;\mathrm{SiO}_{2}&lt;\mathrm{P}_{2} \mathrm{O}_{3}&lt;\mathrm{SO}_{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Al}_{2} \mathrm{O}_{3}&lt;\mathrm{SiO}_{2}&lt;\mathrm{P}_{2} \mathrm{O}_{3}&lt;\mathrm{SO}_{2}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ebJ1lXX8iQocLFz2YT5-cWGQdpuJ-avN5Hg4fLWAbO0.original.fullsize.png"/></div>


title: among-the-following-four-structures-i-to-iv-it-is-true-that-1
slug: among-the-following-four-structures-i-to-iv-it-is-true-that-1-40971
tags: ['Chemistry', 'General Organic Chemistry', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch1_P1.db
question:
<div class="question">Among the following four structures I to IV,
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/RvGKlP_q4aZjgQmNXVsLZT-cY8i1JDj0gRJiVp4Avno.original.fullsize.png"/><br/> <br/> <br/>it is true that</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">only I and II are chiral compounds.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">only III is a chiral compound.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">only II and IV are chiral compounds.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">all four are chiral compounds.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">only I and II are chiral compounds.</span> </div>

answer:
<div class="solution">A chiral object or structure has four different groups attached to the carbon.</div>


title: among-the-following-statements-the-incorrect-one-is
slug: among-the-following-statements-the-incorrect-one-is-42395
question: <div class="question">Among the following statements the incorrect one is:</div>
tags: ['Chemistry', 'General Principles and Processes of Isolation of Metals', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Calamine and siderite are carbonates.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Argentite and cuprite are oxides.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Zinc blende and iron pyrites are sulphides.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Malachite and azurite are ores of copper.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Argentite and cuprite are oxides.</span> </div>

answer:
<div class="solution">Cuprite is $\mathrm{Cu}_{2} \mathrm{O}$ and Argentite is $\mathrm{Ag}_{2} \mathrm{~S}$.</div>


tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch1_P1.db
title:
among-the-following-substituted-silanes-the-one-which-will-give-rise-to-cross-linked-silicone-polymer-on-hydrolysis-is-2

slug:
among-the-following-substituted-silanes-the-one-which-will-give-rise-to-cross-linked-silicone-polymer-on-hydrolysis-is-2-86136

question:
<div class="question">Among the following substituted silanes, the one which will give rise to cross linked silicone polymer on hydrolysis is?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">R</mi><mn>4</mn></msub><mo> </mo><mi>Si</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">R</mi><mo> </mo><msub><mi>SiCl</mi><mn>3</mn></msub></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">R</mi><mn>2</mn></msub><mo> </mo><msub><mi>SiCl</mi><mn>2</mn></msub></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">R</mi><mn>3</mn></msub><mo> </mo><mi>SiCl</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">R</mi><mo> </mo><msub><mi>SiCl</mi><mn>3</mn></msub></math></span> </div>

answer:
<div class="solution"><p>Among the following substituted silanes, the one which will give rise to cross-linked silicone polymer on hydrolysis is trichloroalkylsilane <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>RSiCl</mi><mn>3</mn></msub></math>.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>RSCl</mi><mn>3</mn></msub></math> gives cross-linked silicon polymer on hydrolysis.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/3339b557-90b1-403d-af07-adf5f3a28ca7-image.png" style="width: 600px; height: 315px;"/></p><p> </p></div>


tags: ['Chemistry', 'Coordination Compounds', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch1_P1.db
title:
among-the-following-the-lowest-degree-of-paramagnetism-per-mole-of-the-compound-at-298-k-will-be-shown-by

slug:
among-the-following-the-lowest-degree-of-paramagnetism-per-mole-of-the-compound-at-298-k-will-be-shown-by-59125

question:
<div class="question">Among the following the lowest degree of paramagnetism per mole of the compound at 298 $\mathrm{K}$ will be shown by</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{MnSO}_{4} \cdot 4 \mathrm{H}_{2} \mathrm{O}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{CuSO}_{4} .5 \mathrm{H}_{2} \mathrm{O}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{FeSO}_{4} \cdot 6 \mathrm{H}_{2} \mathrm{O}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{NiSO}_{4} \cdot 6 \mathrm{H}_{2} \mathrm{O}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{CuSO}_{4} .5 \mathrm{H}_{2} \mathrm{O}$</span> </div>

answer:
<div class="solution">$\begin{array}{lllll}\text { Ion } &amp; \mathrm{Mn}^{2+} &amp; \mathrm{Cu}^{2+} &amp; \mathrm{Fe}^{2+} &amp; \mathrm{Ni}^{2+} \\ \text { EC } &amp; 3 d^{5} &amp; 3 d^{9} &amp; 3 d^{6} &amp; 3 d^{8} \\ \text { Number of } &amp; 5 &amp; 1 &amp; 4 &amp; 2\end{array}$ 
<br/>unpaired electron 
<br/>Hence lowest paramagnetism is shown by $\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}$</div>


title: among-the-following-which-have-highest-melting-point
slug: among-the-following-which-have-highest-melting-point-45589
question: <div class="question">Among the following, which have highest melting point?</div>
tags: ['Chemistry', 'Solid State', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">lonic solids</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Pseudo solids</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Molecular solids</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Amorphous solids</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">lonic solids</span> </div>

answer:
<div class="solution"><p>Ionic solids are formed by three dimensional arrangements of positive charged ions i.e. cations and negative charged ions i.e. anions. These ions are held together by coulombic(electrostatic) forces and hence, ionic solids are hard and brittle.</p><p>Ionic solids have highest melting point due to strong electrostatic force of attraction.</p></div>


title: among-the-given-halides-which-one-will-give-same-product-in-both-s-n-1-and-s-n-2-reactions
slug: among-the-given-halides-which-one-will-give-same-product-in-both-s-n-1-and-s-n-2-reactions-30504
tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
answer: <div class="solution">$S_{\mathbb{N}}^2$ and $S_N 1$ same, if $C^{\oplus}$ not rearrange.</div>
source_db: MarksBatch1_P1.db
question:
<div class="question">Among the given halides, which one will give same product in both $\mathrm{S}_{\mathrm{N}} 1$ and $\mathrm{S}_{\mathrm{N}} 2$ reactions.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/e-0_H6EoHB3qRk9FdDKssOdsSZTE3xSiytrCjRW-dPw.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">(III) only</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">(I) and (II)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">(III) and (IV)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">(I), (III) and (IV)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">(III) and (IV)</span> </div>


title: among-the-ligands-nh-3-en-cn-and-co-the-correct-order-of-their-increasing-field-strength-is
slug: among-the-ligands-nh-3-en-cn-and-co-the-correct-order-of-their-increasing-field-strength-is-38494
tags: ['Chemistry', 'Coordination Compounds', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch1_P1.db
question:
<div class="question">Among the ligands $\mathrm{NH}_3$, en, $\mathrm{CN}^{-}$and $\mathrm{CO}$ the correct order of their increasing field strength, is :</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{NH}_3 &lt; $ en $ &lt; \mathrm{CN}^{-} &lt; \mathrm{CO}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{CN}^{-} &lt; \mathrm{NH}_3 &lt; \mathrm{NH}_3 &lt; $ en</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">en $ &lt; \mathrm{CN}^{-} &lt; \mathrm{NH}_3 &lt; \mathrm{CO}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{CO} &lt; \mathrm{NH}_3 &lt; $ en $ &lt; \mathrm{CN}^{-}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{NH}_3 &lt; $ en $ &lt; \mathrm{CN}^{-} &lt; \mathrm{CO}$</span> </div>

answer:
<div class="solution">Ligands can be arranged in a series in the orders of increasing field strength as given below:<br/>Weak field ligands:<br/>$\mathrm{I}^{-} &lt; \mathrm{Br}^{-} &lt; \mathrm{S}^{2-} &lt; \mathrm{SCN} &lt; \mathrm{Cl}^{-} &lt; \mathrm{N}_3^{-}, \mathrm{F}^{-}$ $ &lt; $ Urea, OH $ &lt; $ oxalate<br/>Strong field ligands<br/>$\mathrm{O}^{--} &lt; \mathrm{H}_2 \mathrm{O} &lt; \mathrm{NCS}^{-} &lt; \text {EDTA } &lt; \mathrm{Py}, \mathrm{NH}_3 &lt; $ en $=\mathrm{SO}_3^{-} &lt; $bipy, Phen $ &lt; \mathrm{NO}_2^{-} &lt; \mathrm{CH}_3^{-}$ $ &lt; \mathrm{C}_6 \mathrm{H}_5^{-} &lt; \mathrm{CN}^{-} &lt; \mathrm{CO}$<br/>Such a series is termed as spectrochemical series. It is an experimentally determined series based on the absorption of light by complexes with different ligands.</div>


tags: ['Physics', 'Ray Optics', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch1_P1.db
title:
an-achromatic-convergent-doublet-of-two-lense-in-contact-has-a-power-of-5-d-the-power-of-converging-lens-is-6-d-the-ratio-of-the-dispersive-power-of-t

slug:
an-achromatic-convergent-doublet-of-two-lense-in-contact-has-a-power-of-5-d-the-power-of-converging-lens-is-6-d-the-ratio-of-the-dispersive-power-of-t-12445

question:
<div class="question">An achromatic convergent doublet of two lense in contact has a power of $+5 \mathrm{D}$. The power of converging lens is $+6 \mathrm{D}$. The ratio of the dispersive power of the convergent and divergent lenses is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>$3: 7$
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$2: 3$
<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"> <br/>$1: 5$
<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"> <br/>$5: 3$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$1: 5$
<br/></span> </div>

answer:
<div class="solution">- The condition of achromatism is $W_1 P_1+W_2 P_2=0$
<br/>$$
<br/>\begin{array}{rlrl}
<br/>\Rightarrow &amp; W_1 P_1 &amp; =-W_2 P_2 \\
<br/>\Rightarrow &amp; &amp; \frac{W_1}{W_2} &amp; =-\frac{P_2}{P_1}
<br/>\end{array}
<br/>$$
<br/>Now, $\quad P_1+P_2=4 \mathrm{D}$
<br/>but, Power of converging lens,
<br/>$$
<br/>P_1=5 \mathrm{D}
<br/>$$
<br/>$\because$ Power of diverging lens
<br/>$$
<br/>\begin{aligned}
<br/>P_2 &amp; =4 \mathrm{D}-P_1 \\
<br/>&amp; =4 \mathrm{D}-5 \mathrm{D}=-\mathrm{D}
<br/>\end{aligned}
<br/>$$
<br/>[From ii]
<br/>$\therefore$ From Eq. (i), we have
<br/>$$
<br/>\frac{W_1}{W_2}=-\frac{P_2}{P_1}=\frac{-(-D)}{5 D}=\frac{1}{5} \Rightarrow \frac{W_1}{W_2}=\frac{1}{5}
<br/>$$</div>


tags: ['Physics', 'Motion In One Dimension', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
an-aeroplane-is-flying-in-a-horizontal-direction-with-a-velocity-u-and-at-a-height-of-2000-m-when-it-is-vertically-below-a-point-a-on-the-ground-a-foo-1

slug:
an-aeroplane-is-flying-in-a-horizontal-direction-with-a-velocity-u-and-at-a-height-of-2000-m-when-it-is-vertically-below-a-point-a-on-the-ground-a-foo-1-94691

question:
<div class="question">An aeroplane is flying in a horizontal direction with a velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math> and at a height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2000</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. When it is vertically below a point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> on the ground a food packet is released from it. The packet strikes the ground at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math>. If <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>B</mi><mo>=</mo><mn>3</mn><mo> </mo><mi>km</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mn>10</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></math>, then the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>54</mn><mo> </mo><mi>km</mi><mo> </mo><msup><mi mathvariant="normal">h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>540</mn><mo> </mo><mi>km</mi><mo> </mo><msup><mi mathvariant="normal">h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>150</mn><mo> </mo><mi>km</mi><mo> </mo><msup><mi mathvariant="normal">h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><mo> </mo><mi>km</mi><mo> </mo><msup><mi mathvariant="normal">h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>540</mn><mo> </mo><mi>km</mi><mo> </mo><msup><mi mathvariant="normal">h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </div>

answer:
<div class="solution"><p>Given <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mn>3</mn><mo> </mo><mi>km</mi><mo>=</mo><mn>3000</mn><mo> </mo><mi mathvariant="normal">m</mi></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/d0e544e3-2c92-4ceb-8b42-ecc6f5f9f71f-image.png" style="width: 170px; height: 205px;"/></p><p>Range, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>u</mi><msqrt><mfrac><mrow><mn>2</mn><mi>h</mi></mrow><mi>g</mi></mfrac></msqrt></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mi>u</mi><mo>=</mo><mi>R</mi><msqrt><mfrac><mi>g</mi><mrow><mn>2</mn><mi>h</mi></mrow></mfrac></msqrt></math>or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mn>3000</mn><mo>×</mo><msqrt><mfrac><mn>10</mn><mrow><mn>2</mn><mo>×</mo><mn>2000</mn></mrow></mfrac></msqrt></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3000</mn><mo>×</mo><mfrac><mn>1</mn><mn>20</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>150</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>150</mn><mo>×</mo><mfrac><mn>18</mn><mn>5</mn></mfrac><mo> </mo><mi>km</mi><mo> </mo><msup><mi mathvariant="normal">h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>540</mn><mo> </mo><mi>km</mi><mo> </mo><msup><mi mathvariant="normal">h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p></div>


tags: ['Physics', 'Motion In One Dimension', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P1.db
title:
an-aeroplane-is-flying-in-a-horizontal-direction-with-a-velocity-u-and-at-a-height-of-2000-m-when-it-is-vertically-below-a-point-a-on-the-ground-a-foo

slug:
an-aeroplane-is-flying-in-a-horizontal-direction-with-a-velocity-u-and-at-a-height-of-2000-m-when-it-is-vertically-below-a-point-a-on-the-ground-a-foo-28165

question:
<div class="question">An aeroplane is flying in a horizontal direction with a velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math> and at a height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2000</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. When it is vertically below a point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> on the ground a food packet is released from it. The packet strikes the ground at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math>. If <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>B</mi><mo>=</mo><mn>3</mn><mo> </mo><mi>km</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mn>10</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></math>, then the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>54</mn><mo> </mo><mi>km</mi><mo> </mo><msup><mi mathvariant="normal">h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>540</mn><mo> </mo><mi>km</mi><mo> </mo><msup><mi mathvariant="normal">h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>150</mn><mo> </mo><mi>km</mi><mo> </mo><msup><mi mathvariant="normal">h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><mo> </mo><mi>km</mi><mo> </mo><msup><mi mathvariant="normal">h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>540</mn><mo> </mo><mi>km</mi><mo> </mo><msup><mi mathvariant="normal">h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </div>

answer:
<div class="solution"><p>Given <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mn>3</mn><mo> </mo><mi>km</mi><mo>=</mo><mn>3000</mn><mo> </mo><mi mathvariant="normal">m</mi></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/d0e544e3-2c92-4ceb-8b42-ecc6f5f9f71f-image.png" style="width: 170px; height: 205px;"/></p><p>Range, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>u</mi><msqrt><mfrac><mrow><mn>2</mn><mi>h</mi></mrow><mi>g</mi></mfrac></msqrt></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mi>u</mi><mo>=</mo><mi>R</mi><msqrt><mfrac><mi>g</mi><mrow><mn>2</mn><mi>h</mi></mrow></mfrac></msqrt></math>or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mn>3000</mn><mo>×</mo><msqrt><mfrac><mn>10</mn><mrow><mn>2</mn><mo>×</mo><mn>2000</mn></mrow></mfrac></msqrt></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3000</mn><mo>×</mo><mfrac><mn>1</mn><mn>20</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>150</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>150</mn><mo>×</mo><mfrac><mn>18</mn><mn>5</mn></mfrac><mo> </mo><mi>km</mi><mo> </mo><msup><mi mathvariant="normal">h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>540</mn><mo> </mo><mi>km</mi><mo> </mo><msup><mi mathvariant="normal">h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p></div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch1_P1.db
title:
an-air-bubble-of-volume-v-0-is-released-by-a-fish-at-a-depth-h-in-a-lake-the-bubble-rises-to-the-surface-assume-constant-temperature-and-standard-atmo

slug:
an-air-bubble-of-volume-v-0-is-released-by-a-fish-at-a-depth-h-in-a-lake-the-bubble-rises-to-the-surface-assume-constant-temperature-and-standard-atmo-22957

question:
<div class="question">An air bubble of volume $\mathrm{v}_{0}$ is released by a fish at a depth $\mathrm{h}$ in a lake. The bubble rises to the surface. Assume constant temperature and standard atmospheric pressure above the lake. The volume of the bubble just before touching the surface will be (density) of water is $\rho$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{v}_{0}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\quad v_{0}(\rho g h / p)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\mathrm{v}_{0}}{\left(1+\frac{\rho \mathrm{gh}}{\mathrm{p}}\right)}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{v}_{0}\left(1+\frac{\rho \mathrm{gh}}{\mathrm{p}}\right)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{v}_{0}\left(1+\frac{\rho \mathrm{gh}}{\mathrm{p}}\right)$</span> </div>

answer:
<div class="solution">As the bubble rises the pressure gets reduced for constant temperature, if $\mathrm{P}$ is the standard atmospheric pressure, then $(\mathrm{P}+\rho \mathrm{gh}) \mathrm{V}_{0}=\mathrm{PV}$<br/>$$<br/>\text { or } \mathrm{V}=\mathrm{V}_{0}\left(1+\frac{\rho \mathrm{gh}}{\mathrm{P}}\right)<br/>$$</div>


tags: ['Physics', 'Alternating Current', 'BITSAT', 'BITSAT 2010']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">zero</span> </div>
source_db: MarksBatch1_P1.db
title:
an-alternating-voltage-v-v-0-sin-ot-is-appliedacross-a-circuit-as-a-result-a-current-i-i-0-sin-t-2-flows-in-it-the-power-consumed-per-cycle-is

slug:
an-alternating-voltage-v-v-0-sin-ot-is-appliedacross-a-circuit-as-a-result-a-current-i-i-0-sin-t-2-flows-in-it-the-power-consumed-per-cycle-is-81448

question:
<div class="question">An alternating voltage $V=V_{0}$ sin ot is appliedacross a circuit. As a result, a current $I=I_{0} \sin (\omega t-\pi / 2)$ flows in it. The power consumed per cycle is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">zero</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.5 \mathrm{~V}_{0} \mathrm{I}_{0}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0.707 \mathrm{~V}_{0} \mathrm{I}_{0}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1.414 \mathrm{~V}_{0} \mathrm{I}_{0}$</span> </li> </ul>

answer:
<div class="solution">The phase angle between voltage $\mathrm{V}$ and current I is $\pi / 2$.</div>


tags: ['Physics', 'Alternating Current', 'BITSAT', 'BITSAT 2021']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">zero</span> </div>
source_db: MarksBatch1_P1.db
title:
an-alternating-voltage-v-v-0-sin-t-is-applied-across-a-circuit-as-a-result-a-current-i-i-0-sin-t-2-flows-in-it-the-power-consumed-per-cycle-is

slug:
an-alternating-voltage-v-v-0-sin-t-is-applied-across-a-circuit-as-a-result-a-current-i-i-0-sin-t-2-flows-in-it-the-power-consumed-per-cycle-is-82895

question:
<div class="question">An alternating voltage $\mathrm{V}=\mathrm{V}_{0} \sin \omega \mathrm{t}$ is applied across a circuit. As a result, a current $\mathrm{I}=\mathrm{I}_{0} \sin \left(\omega \mathrm{t}-\frac{\pi}{2}\right)$ flows in it. The power consumed per cycle is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">zero</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.5 \mathrm{~V}_{0} \mathrm{I}_{0}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0.707 \mathrm{~V}_{0} \mathrm{I}_{0}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1.414 \mathrm{~V}_{0} \mathrm{I}_{0}$</span> </li> </ul>

answer:
<div class="solution">The phase angle between voltage $V$ and current $I$ is $\frac{\pi}{2}$.
<br/> <br/>Therefore, power factor $\cos \phi=\cos \left(\frac{\pi}{2}\right)=0$.
<br/> <br/>Hence the power consumed is zero.</div>


tags: ['Physics', 'Current Electricity', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch1_P1.db
title:
an-ammeter-of-resistance-1-5-can-measure-currents-upto-1-a-the-value-of-shunt-resistance-to-measure-current-upto-4-a-is

slug:
an-ammeter-of-resistance-1-5-can-measure-currents-upto-1-a-the-value-of-shunt-resistance-to-measure-current-upto-4-a-is-72641

question:
<div class="question">An ammeter of resistance <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math> can measure currents upto <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">A</mi></math>. The value of shunt resistance to measure current upto <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mi mathvariant="normal">A</mi></math> is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>2</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></span> </div>

answer:
<div class="solution"><p>Given, for an ammeter, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mi>g</mi></msub><mo>=</mo><mn>1</mn><mo> </mo><mi mathvariant="normal">A</mi><mo>,</mo><mo> </mo><msub><mi>R</mi><mi>g</mi></msub><mo>=</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></p><p>Total current, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mn>4</mn><mo> </mo><mi mathvariant="normal">A</mi></math></p><p>If <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mi>s</mi></msub></math> be the shunt resistance, then according to the question circuit diagram is given, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close=""><mrow><msub><mi>R</mi><mi>s</mi></msub><mo>‖</mo><msub><mi>R</mi><mi>g</mi></msub><mo>,</mo></mrow></mfenced></math> hence have equal potential difference<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>)</mo></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/628a806f-5173-4697-b3d9-2c930f3dee17-d47.png" style="width: 348px; height: 170px;"/></p><p>where, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mi>g</mi></msub><msub><mi>R</mi><mi>g</mi></msub><mo>=</mo><mfenced><mrow><mi>I</mi><mo>-</mo><msub><mi>I</mi><mi>g</mi></msub></mrow></mfenced><msub><mi>R</mi><mi>s</mi></msub></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mi>s</mi></msub><mo>=</mo><mfrac><msub><mi>I</mi><mi>g</mi></msub><mrow><mi>I</mi><mo>-</mo><msub><mi>I</mi><mi>g</mi></msub></mrow></mfrac><mo>×</mo><msub><mi>R</mi><mi>g</mi></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>4</mn><mo>-</mo><mn>1</mn></mrow></mfrac><mo>×</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></p></div>


tags: ['Physics', 'Current Electricity', 'BITSAT', 'BITSAT 2009']
answer: <div class="solution">No Solution available</div>
source_db: MarksBatch1_P1.db
title:
an-ammeter-reads-upto-1-ampere-its-internal-resistance-is-081-ohm-to-increase-the-range-to-10-a-the-value-of-the-required-shunt-is

slug:
an-ammeter-reads-upto-1-ampere-its-internal-resistance-is-081-ohm-to-increase-the-range-to-10-a-the-value-of-the-required-shunt-is-59744

question:
<div class="question">An ammeter reads upto 1 ampere. Its internal resistance is $0.81 \mathrm{ohm} .$ To increase the range to 10 A the value of the required shunt is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.03 \Omega$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.3 \Omega$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0.9 \Omega$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$0.09 \Omega$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.09 \Omega$</span> </div>


tags: ['Chemistry', 'Solutions', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch1_P1.db
title:
an-aqueous-solution-freezes-at-272-4-k-while-pure-water-freezes-at-273-k-given-k-f-1-86-k-kg-mol-1-and-k-b-0-512-k-kg-mol-1-the-molality-of-solution-a

slug:
an-aqueous-solution-freezes-at-272-4-k-while-pure-water-freezes-at-273-k-given-k-f-1-86-k-kg-mol-1-and-k-b-0-512-k-kg-mol-1-the-molality-of-solution-a-42630

question:
<div class="question">An aqueous solution freezes at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>272</mn><mo>.</mo><mn>4</mn><mo> </mo><mi mathvariant="normal">K</mi></math>, while pure water freezes at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>273</mn><mo> </mo><mi mathvariant="normal">K</mi></math>, given <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mi mathvariant="normal">f</mi></msub><mo>=</mo><mn>1</mn><mo>.</mo><mn>86</mn><mo> </mo><mi mathvariant="normal">K</mi><mo> </mo><mi>kg</mi><mo> </mo><msup><mi>mol</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mi mathvariant="normal">b</mi></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>512</mn><mo> </mo><mi mathvariant="normal">K</mi><mo> </mo><mi>kg</mi><mo> </mo><msup><mi>mol</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>;</mo></math> the molality of solution and boiling point of solution respectively will be -</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>322</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>373</mn><mo>.</mo><mn>16</mn><mo> </mo><mi mathvariant="normal">K</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>222</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>273</mn><mo>.</mo><mn>15</mn><mo> </mo><mi mathvariant="normal">K</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>413</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>400</mn><mo> </mo><mi mathvariant="normal">K</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><mo>.</mo><mn>73</mn><mo> </mo><mi mathvariant="normal">K</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>322</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>373</mn><mo>.</mo><mn>16</mn><mo> </mo><mi mathvariant="normal">K</mi></math></span> </div>

answer:
<div class="solution"><p>Depression in freezing point is given as <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ΔT</mi><mi mathvariant="normal">f</mi></msub><mo>=</mo><msub><mi mathvariant="normal">K</mi><mi mathvariant="normal">f</mi></msub><mi mathvariant="normal">m</mi></math></p><p>Molality of solution <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi mathvariant="normal">m</mi></mfenced><mo>=</mo><mfrac><msub><mi>ΔT</mi><mi mathvariant="normal">f</mi></msub><msub><mi mathvariant="normal">K</mi><mi mathvariant="normal">f</mi></msub></mfrac></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>6</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>86</mn></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>322</mn><mo> </mo><mi mathvariant="normal">m</mi></math></p><p>Elevation in boiling point of solution is given as</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ΔT</mi><mi mathvariant="normal">b</mi></msub><mo>=</mo><msub><mi mathvariant="normal">k</mi><mi mathvariant="normal">b</mi></msub><mo>×</mo><mi mathvariant="normal">m</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ΔT</mi><mi mathvariant="normal">b</mi></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>512</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>322</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ΔT</mi><mi mathvariant="normal">b</mi></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>165</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Boiling point of solution <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>373</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>16</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>373</mn><mo>.</mo><mn>16</mn><mo> </mo><mi mathvariant="normal">K</mi></math></p></div>


tags: ['Chemistry', 'Practical Chemistry', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch1_P1.db
title:
an-aqueous-solution-of-a-substance-gives-a-white-precipitate-on-treatment-with-dil-hcl-which-dissolves-on-heating-when-h-2-s-is-passed-through-the-hot

slug:
an-aqueous-solution-of-a-substance-gives-a-white-precipitate-on-treatment-with-dil-hcl-which-dissolves-on-heating-when-h-2-s-is-passed-through-the-hot-81874

question:
<div class="question">An aqueous solution of a substance gives a white precipitate on treatment with dil. HCl which dissolves on heating. When $\mathrm{H}_{2} \mathrm{~S}$ is passed through the hot acidic solution, a black precipitate is obtained. The substance is a</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{Hg}_{2}^{2+}$ salt</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{Cu}^{2+}$ salt</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Ag}^{+}$ salt</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{Pb}^{2+}$ salt</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Pb}^{2+}$ salt</span> </div>

answer:
<div class="solution">$\mathrm{PbCl}_{2}$ is insoluble in cold water, soluble in hot water and $\mathrm{PbS}$ is black ppt in acidic medium.</div>


tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P1.db
title:
an-arch-of-a-bridge-is-semielliptical-with-major-axis-horizontal-if-the-length-the-base-is-9-meter-and-the-highest-part-of-the-bridge-is-3-meter-from-

slug:
an-arch-of-a-bridge-is-semielliptical-with-major-axis-horizontal-if-the-length-the-base-is-9-meter-and-the-highest-part-of-the-bridge-is-3-meter-from-14505

question:
<div class="question">An arch of a bridge is semi-elliptical with major axis horizontal. If the length the base is 9 meter and the highest part of the bridge is 3 meter from the horizontal; the best approximation of the height of the arch. 2 meter from the centre of the base is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$11 / 4 \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$8 / 3 \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$7 / 2 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$8 / 3 \mathrm{~m}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/2hq8a_AlD6WCdS2CUiDQ8R63IEfVVdLzZaSb81arPZ0.original.fullsize.png"/><br/> <br/> <br/>The equation of the ellipse is
<br/> <br/>$$
<br/> <br/>\frac{x^{2}}{\left(\frac{9}{2}\right)^{2}}+\frac{y^{2}}{9}=1
<br/> <br/>$$
<br/> <br/>Where centre is assumed as origin and base as $x$ -axis. Put $x=2,$ we get
<br/> <br/>$$
<br/> <br/>\frac{16}{81}+\frac{\mathrm{y}^{2}}{9}=1 \Rightarrow \mathrm{y}=\frac{\sqrt{65}}{3} \approx \frac{8}{3} \mathrm{~m}
<br/> <br/>$$
<br/> <br/>(approximately)</div>


tags: ['Chemistry', 'General Organic Chemistry', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch1_P1.db
title:
an-aromatic-compound-has-molecular-formula-c-7-h-7-br-give-the-possible-isomers-and-the-appropriate-method-to-distinguish-them

slug:
an-aromatic-compound-has-molecular-formula-c-7-h-7-br-give-the-possible-isomers-and-the-appropriate-method-to-distinguish-them-27153

question:
<div class="question">An aromatic compound has molecular formula $\mathrm{C}_{7} \mathrm{H}_{7} \mathrm{Br}$. Give the possible isomers and the appropriate method to distinguish them.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">3 isomers; by heating with $\mathrm{AgNO}_{3}$ solution</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">4 isomers; by treating with $\mathrm{AgNO}_{3}$ solution</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">4 isomers; by oxidation</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">5 isomers; by oxidation</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">4 isomers; by oxidation</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/rxdi4eb42TTeYE9QPzNfNl9R00rtjsiCkz9xapd_FfI.original.fullsize.png"/></div>


tags: ['Physics', 'Gravitation', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch1_P1.db
title:
an-artificial-satellite-is-moving-in-a-circular-orbit-around-the-earth-with-a-speed-equal-to-half-the-magnitude-of-the-escape-velocity-from-the-earth-

slug:
an-artificial-satellite-is-moving-in-a-circular-orbit-around-the-earth-with-a-speed-equal-to-half-the-magnitude-of-the-escape-velocity-from-the-earth-35712

question:
<div class="question">An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth. The height $(h)$ of the satellite above the earth's surface is (Take radius of earth as $R_{e}$ )</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$h=R_{e}^{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$h=R_{e}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$h=2 R_{e}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$h=4 R_{e}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$h=R_{e}$</span> </div>

answer:
<div class="solution">The escape velocity from earth is given by $v_{e}=\sqrt{2 \mathrm{~g} R_{e}} \ldots$ (i)
<br/> <br/>The orbital velocity of a satellite revolving around earth is given by
<br/> <br/>$$
<br/> <br/>v_{0}=\frac{\sqrt{\mathrm{G} M_{e}}}{\left(R_{e}+h\right)}
<br/> <br/>$$
<br/> <br/>where, $M_{e}=$ mass of earth, $R_{e}=$ radius of earth, $h=$ height of satellite from surface of earth.
<br/> <br/>By the relation $\mathrm{G} M_{e}=\mathrm{g} R_{e}^{2}$
<br/> <br/>$$
<br/> <br/>\text { So, } \quad v_{0}=\frac{\sqrt{g R_{e}^{2}}}{\left(R_{e}+h\right)} \ldots
<br/> <br/>$$
<br/> <br/>Dividing equation (i) by (ii), we get
<br/> <br/>$$
<br/> <br/>\frac{v_{e}}{v_{0}}=\frac{\sqrt{2\left(R_{e}+h\right)}}{\left(R_{e}\right)}
<br/> <br/>$$
<br/> <br/>Given, $v_{0}=\frac{v_{e}}{2}$
<br/> <br/>$$
<br/> <br/>\frac{2 v_{e}}{v_{e}}=\frac{\sqrt{2\left(R_{e}+h\right)}}{R_{e}}
<br/> <br/>$$
<br/> <br/>Squaring on both side, we get
<br/> <br/>$$
<br/> <br/>4=\frac{2\left(R_{e}+h\right)}{R_{e}}
<br/> <br/>$$
<br/> <br/>or $R_{e}+h=2 R_{e} \quad$ i.e., $h=R_{e}$</div>


tags: ['Physics', 'Gravitation', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch1_P1.db
title:
an-asteroid-of-mass-m-is-approaching-earth-initially-at-a-distance-10-r-e-with-speed-v-i-it-hite-oarth-with-a-speed-v-f-r-e-and-m-e-are-radius-and-mas

slug:
an-asteroid-of-mass-m-is-approaching-earth-initially-at-a-distance-10-r-e-with-speed-v-i-it-hite-oarth-with-a-speed-v-f-r-e-and-m-e-are-radius-and-mas-62954

question:
<div class="question">An asteroid of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> is approaching earth, initially at a distance <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><msub><mi>R</mi><mi>e</mi></msub></math> with speed <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>i</mi></msub><mo>.</mo></math> It hite oarth with a speed <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>f</mi></msub><mo> </mo><mo>,</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close=""><msub><mi>R</mi><mi>e</mi></msub></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>M</mi><mi>e</mi></msub></math> are radius and mass of earth<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>)</mo></math>, then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>v</mi><mi>f</mi><mn>2</mn></msubsup><mo>=</mo><msubsup><mi>v</mi><mi>i</mi><mn>2</mn></msubsup><mo>+</mo><mfrac><mrow><mn>2</mn><mi>G</mi><mi>m</mi></mrow><msub><mi>R</mi><mi>e</mi></msub></mfrac><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><mn>10</mn></mfrac></mrow></mfenced></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>v</mi><mi>f</mi><mn>2</mn></msubsup><mo>=</mo><msubsup><mi>v</mi><mi>i</mi><mn>2</mn></msubsup><mo>+</mo><mfrac><mrow><mn>2</mn><mi>G</mi><msub><mi>M</mi><mi>e</mi></msub></mrow><msub><mi>R</mi><mi>e</mi></msub></mfrac><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><mn>10</mn></mfrac></mrow></mfenced></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>v</mi><mi>f</mi><mn>2</mn></msubsup><mo>=</mo><msubsup><mi>v</mi><mi>i</mi><mn>2</mn></msubsup><mo>+</mo><mfrac><mrow><mn>2</mn><mi>G</mi><msub><mi>M</mi><mi>e</mi></msub></mrow><msub><mi>R</mi><mi>θ</mi></msub></mfrac><mfenced><mrow><mn>1</mn><mo>-</mo><mfrac><mn>1</mn><mn>10</mn></mfrac></mrow></mfenced></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>v</mi><mi>f</mi><mn>2</mn></msubsup><mo>=</mo><msubsup><mi>v</mi><mi>i</mi><mn>2</mn></msubsup><mo>+</mo><mfrac><mrow><mn>2</mn><mi>G</mi><mi>m</mi></mrow><msub><mi>R</mi><mi>e</mi></msub></mfrac><mfenced><mrow><mn>1</mn><mo>-</mo><mfrac><mn>1</mn><mn>10</mn></mfrac></mrow></mfenced></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>v</mi><mi>f</mi><mn>2</mn></msubsup><mo>=</mo><msubsup><mi>v</mi><mi>i</mi><mn>2</mn></msubsup><mo>+</mo><mfrac><mrow><mn>2</mn><mi>G</mi><msub><mi>M</mi><mi>e</mi></msub></mrow><msub><mi>R</mi><mi>θ</mi></msub></mfrac><mfenced><mrow><mn>1</mn><mo>-</mo><mfrac><mn>1</mn><mn>10</mn></mfrac></mrow></mfenced></math></span> </div>

answer:
<div class="solution"><p>Initial energy of the asteroid is<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>i</mi></msub><mo>=</mo><msub><mi>K</mi><mi>i</mi></msub><mo>+</mo><msub><mi>U</mi><mi>i</mi></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>m</mi><msubsup><mi>v</mi><mi>i</mi><mn>2</mn></msubsup><mo>-</mo><mfrac><mrow><mi>G</mi><msub><mi>M</mi><mi>θ</mi></msub><mi>m</mi></mrow><mrow><mn>10</mn><msub><mi>R</mi><mi>e</mi></msub></mrow></mfrac></math></p><p>Final energy of the asteroid,<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>f</mi></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>m</mi><msubsup><mi>v</mi><mi>f</mi><mn>2</mn></msubsup><mo>-</mo><mfrac><mrow><mi>G</mi><msub><mi>M</mi><mi>θ</mi></msub><mi>m</mi></mrow><msub><mi>R</mi><mi>θ</mi></msub></mfrac></math></p><p>According to law of conservation of energy, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>i</mi></msub><mo>=</mo><msub><mi>E</mi><mi>f</mi></msub></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>m</mi><msubsup><mi>v</mi><mi>i</mi><mn>2</mn></msubsup><mo>-</mo><mfrac><mrow><mi>G</mi><msub><mi>M</mi><mi>θ</mi></msub><mi>m</mi></mrow><mrow><mn>10</mn><msub><mi>R</mi><mi>θ</mi></msub></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>m</mi><msubsup><mi>v</mi><mi>f</mi><mn>2</mn></msubsup><mo>-</mo><mfrac><mrow><mi>G</mi><msub><mi>M</mi><mi>θ</mi></msub><mi>m</mi></mrow><msub><mi>R</mi><mi>θ</mi></msub></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>v</mi><mi>f</mi><mn>2</mn></msubsup><mo>-</mo><mfrac><mrow><mn>2</mn><mi>G</mi><msub><mi>M</mi><mi>θ</mi></msub></mrow><msub><mi>R</mi><mi>θ</mi></msub></mfrac><mo>=</mo><msubsup><mi>v</mi><mi>i</mi><mn>2</mn></msubsup><mo>-</mo><mfrac><mrow><mn>2</mn><mi>G</mi><msub><mi>M</mi><mi>θ</mi></msub></mrow><mrow><mn>10</mn><msub><mi>R</mi><mi>θ</mi></msub></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msubsup><mi>v</mi><mi>f</mi><mn>2</mn></msubsup><mo>=</mo><msubsup><mi>v</mi><mi>i</mi><mn>2</mn></msubsup><mo>+</mo><mfrac><mrow><mn>2</mn><mi>G</mi><msub><mi>M</mi><mi>θ</mi></msub></mrow><msub><mi>R</mi><mi>θ</mi></msub></mfrac><mfenced><mrow><mn>1</mn><mo>-</mo><mfrac><mn>1</mn><mn>10</mn></mfrac></mrow></mfenced></math></p></div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch1_P1.db
title:
an-automobile-moving-with-a-speed-of-36-km-h-1-reaches-an-upward-inclined-road-of-angle-30-its-engine-becomes-switch-off-if-the-coefficient-of-frictio

slug:
an-automobile-moving-with-a-speed-of-36-km-h-1-reaches-an-upward-inclined-road-of-angle-30-its-engine-becomes-switch-off-if-the-coefficient-of-frictio-37370

question:
<div class="question">An automobile moving with a speed of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn><mo> </mo><mi>km</mi><mo> </mo><msup><mi mathvariant="normal">h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> reaches an upward inclined road of angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo>°</mo><mo>,</mo></math> its engine becomes switch off. If the coefficient of friction is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>1</mn></math>, then how much distance will automobile move before coming to rest?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>.</mo><mn>53</mn><mo> </mo><mi mathvariant="normal">m</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>21</mn><mo>.</mo><mn>42</mn><mo> </mo><mi mathvariant="normal">m</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>.</mo><mn>43</mn><mo> </mo><mi mathvariant="normal">m</mi></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>53</mn><mo> </mo><mi mathvariant="normal">m</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>53</mn><mo> </mo><mi mathvariant="normal">m</mi></math></span> </div>

answer:
<div class="solution"><p>Given, initial speed, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mn>36</mn><mo> </mo><mi>km</mi><mo> </mo><msup><mi mathvariant="normal">h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>36</mn><mo>×</mo><mn>1000</mn></mrow><mrow><mn>60</mn><mo>×</mo><mn>60</mn></mrow></mfrac><mo>=</mo><mn>10</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/fbc09836-081b-4499-8a48-2d318e120ee6-image.png" style="width: 240px; height: 180px;"/></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mn>30</mn><mo>°</mo><mo>,</mo><mo> </mo><mi>μ</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>,</mo><mo> </mo><mi>s</mi><mo>=</mo><mo>?</mo></math></p><p>Here, work done in moving up the inclined road<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo> </mo><mi>K</mi><mi>E</mi></math> of the vehicle</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>m</mi><mi>g</mi><mo> </mo><mi>sin</mi><mo> </mo><mi>θ</mi><mo>+</mo><mi>F</mi></mrow></mfenced><mo> </mo><mi>s</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>m</mi><msup><mi>u</mi><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>m</mi><mi>g</mi><mo> </mo><mi>sin</mi><mo> </mo><mi>θ</mi><mo>+</mo><mi>μ</mi><mi>R</mi></mrow></mfenced><mo>×</mo><mi>s</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>m</mi><msup><mi>u</mi><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>m</mi><mi>g</mi><mo> </mo><mi>sin</mi><mo> </mo><mi>θ</mi><mo>+</mo><mi>μ</mi><mo> </mo><mi>m</mi><mi>g</mi><mo> </mo><mi>cos</mi><mo> </mo><mi>θ</mi></mrow></mfenced><mo>×</mo><mi>s</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>m</mi><msup><mi>u</mi><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mfrac><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>m</mi><msup><mi>u</mi><mn>2</mn></msup></mrow><mrow><mi>m</mi><mi>g</mi><mo> </mo><mfenced><mrow><mi>sin</mi><mo> </mo><mi>θ</mi><mo>+</mo><mi>μ</mi><mo> </mo><mi>cos</mi><mo> </mo><mi>θ</mi></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><msup><mi>u</mi><mn>2</mn></msup><mrow><mn>2</mn><mo> </mo><mi mathvariant="normal">g</mi><mo> </mo><mfenced><mrow><mi>sin</mi><mo> </mo><mi>θ</mi><mo>+</mo><mi>μ</mi><mo> </mo><mi>cos</mi><mo> </mo><mi>θ</mi></mrow></mfenced></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>10</mn><mo>×</mo><mn>10</mn></mrow><mrow><mn>2</mn><mo>×</mo><mn>10</mn><mo>×</mo><mo> </mo><mfenced><mrow><mi>sin</mi><mo> </mo><mn>30</mn><mo>°</mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo> </mo><mi>cos</mi><mo> </mo><mn>30</mn><mo>°</mo></mrow></mfenced></mrow></mfrac><mo>=</mo><mn>8</mn><mo>.</mo><mn>53</mn><mo> </mo><mi mathvariant="normal">m</mi></math></p></div>


title: an-e-has-magnetic-quantum-number-as-3-what-is-its-principal-quantum-number
slug: an-e-has-magnetic-quantum-number-as-3-what-is-its-principal-quantum-number-52152
tags: ['Chemistry', 'Structure of Atom', 'BITSAT', 'BITSAT 2016']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
answer: <div class="solution">When $m=-3, l=3, \therefore \mathrm{n}=4$.</div>
source_db: MarksBatch1_P1.db
question:
<div class="question">An e $^{-}$ has magnetic quantum number as $-3,$ what is its principal quantum number?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">3</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">4</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>


tags: ['Physics', 'Work Power Energy', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch1_P1.db
title:
an-elastic-string-of-unstretched-length-l-and-force-constant-k-is-stretched-by-a-small-length-x-it-is-further-stretched-by-another-small-length-y-the-

slug:
an-elastic-string-of-unstretched-length-l-and-force-constant-k-is-stretched-by-a-small-length-x-it-is-further-stretched-by-another-small-length-y-the-56019

question:
<div class="question">An elastic string of unstretched length $\mathrm{L}$ and force constant $\mathrm{k}$ is stretched by a small length $\mathrm{x}$. It is further stretched by another small length y. The work done in the second stretching is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 / 2 \mathrm{Ky}^{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$1 / 2 \mathrm{Ky}(2 \mathrm{x}+\mathrm{y})$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1 / 2 \mathrm{~K}\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1 / 2 \mathrm{k}(\mathrm{x}+\mathrm{y})^{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1 / 2 \mathrm{Ky}(2 \mathrm{x}+\mathrm{y})$</span> </div>

answer:
<div class="solution">In the string elastic force is conservative in nature. $\therefore \mathrm{W}=-\Delta \mathrm{U}$
<br/> <br/>Work done by elastic force of string,
<br/> <br/>$$
<br/> <br/>\begin{aligned}
<br/> <br/>\mathrm{W} &amp;=-\left(\mathrm{U}_{\mathrm{F}}-\mathrm{U}_{\mathrm{i}}\right)=\mathrm{U}_{\mathrm{i}}-\mathrm{U}_{\mathrm{F}} \\
<br/> <br/>\mathrm{W} &amp;=\frac{1}{2} \mathrm{k} \mathrm{x}^{2}-\frac{\mathrm{k}}{2}(\mathrm{x}+\mathrm{y})^{2} \\
<br/> <br/>&amp;=\frac{1}{2} \mathrm{k} \mathrm{x}^{2}-\frac{1}{2} \mathrm{k}\left(\mathrm{x}^{2}+\mathrm{y}^{2}+2 \mathrm{xy}\right) \\
<br/> <br/>&amp;=\frac{1}{2} \mathrm{k} \mathrm{x}^{2}-\frac{1}{2} \mathrm{k} \mathrm{y}^{2}-\frac{1}{2} \mathrm{kx}^{2}-\frac{1}{2} \mathrm{k}(2 \mathrm{xy}) \\
<br/> <br/>&amp;=-\mathrm{k} \mathrm{x} \mathrm{y}-\frac{1}{2} \mathrm{k} \mathrm{y}^{2}
<br/> <br/>\end{aligned}
<br/> <br/>$$
<br/> <br/>Therefore, the work done against elastic force
<br/> <br/>$\mathrm{W}_{\text {external }}=-\mathrm{W}=\frac{\mathrm{K} y}{2}(2 \mathrm{x}+\mathrm{y})$</div>


tags: ['Physics', 'Current Electricity', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch1_P1.db
title:
an-electric-current-i-enters-and-leaves-a-uniform-circular-wire-of-radius-r-through-diametrically-opposite-points-a-charged-particle-q-moves-along-the

slug:
an-electric-current-i-enters-and-leaves-a-uniform-circular-wire-of-radius-r-through-diametrically-opposite-points-a-charged-particle-q-moves-along-the-30274

question:
<div class="question">An electric current $I$ enters and leaves a uniform circular wire of radius $r$ through diametrically opposite points. A charged particle $q$ moves along the axis of circular wire passes through its centre at speed $v$.
<br/>The magnetic force on the particle when it passes through the centre has a magnitude.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>$\frac{q v \mu_0 I}{2 \pi r}$
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/> $q v \frac{\mu_o I}{\pi r}$
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$q v \mu_0 I$
<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"> <br/>0</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>0</span> </div>

answer:
<div class="solution">Force on a moving charged particle in uniform magnetic field
<br/>$$
<br/>F=B q v \sin \theta
<br/>$$
<br/>Since, charge particle moves along the axis of circular current carrying loop, therefore, $\theta=0^{\circ}$ or $180^{\circ}$
<br/>When $\theta=0^{\circ} ; F=B q v \sin 0^{\circ}$
<br/>$$
<br/>F=0
<br/>$$
<br/>When $\theta=180^{\circ}, F=B q u \sin 180^{\circ}$
<br/>$$
<br/>F=0
<br/>$$</div>


tags: ['Physics', 'Electromagnetic Waves', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch1_P1.db
title:
an-electromagnetic-wave-is-propagating-along-x-axis-at-x-1-cm-and-t-18-s-its-electric-vector-e-8-v-m-then-the-magnitude-of-its-magnetic-vector-is

slug:
an-electromagnetic-wave-is-propagating-along-x-axis-at-x-1-cm-and-t-18-s-its-electric-vector-e-8-v-m-then-the-magnitude-of-its-magnetic-vector-is-32659

question:
<div class="question">An electromagnetic wave is propagating along $X$-axis. At $x=1 \mathrm{~cm}$ and $t=18 \mathrm{~s}$, its electric vector $|E|=8 \mathrm{~V} / \mathrm{m}$, then the magnitude of its magnetic vector is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"> <br/>$266 \times 10^{-8}$
<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$3 \times 10^{-7}$
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$3.14 \times 10^{-8}$
<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"> <br/>$3.16 \times 10^{-7}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$266 \times 10^{-8}$
<br/></span> </div>

answer:
<div class="solution">As we know that, $\frac{E}{B}=c$
<br/>$$
<br/>\text { so, } B=\frac{E}{c}=\frac{8}{3 \times 10^8}=2.66 \times 10^{-8}
<br/>$$</div>


tags: ['Physics', 'Electromagnetic Waves', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch1_P1.db
title:
an-electromagnetic-wave-passes-through-space-and-its-equation-is-given-by-e-e-0-sin-t-kx-where-e-is-electric-field-energy-density-of-electromagnetic-w

slug:
an-electromagnetic-wave-passes-through-space-and-its-equation-is-given-by-e-e-0-sin-t-kx-where-e-is-electric-field-energy-density-of-electromagnetic-w-11260

question:
<div class="question">An electromagnetic wave passes through space and its equation is given by $\mathrm{E}=\mathrm{E}_{0} \sin (\omega \mathrm{t}-\mathrm{kx})$<br/>where $\mathrm{E}$ is electric field. Energy density of electromagnetic wave in space is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{1}{2} \varepsilon_{0} \mathrm{E}_{0}^{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{4} \varepsilon_{0} \mathrm{E}_{0}^{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\varepsilon_{0} \mathrm{E}_{0}^{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 \varepsilon_{0} \mathrm{E}_{0}^{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{2} \varepsilon_{0} \mathrm{E}_{0}^{2}$</span> </div>

answer:
<div class="solution">Energy density<br/>$$<br/>=\varepsilon_{0} \mathrm{E}_{\mathrm{rm}}^{2}=\varepsilon_{0}\left(\frac{\mathrm{E}_{0}}{\sqrt{2}}\right)^{2}=\frac{1}{2} \varepsilon_{0} \mathrm{E}_{0}^{2}<br/>$$</div>


tags: ['Physics', 'Dual Nature of Matter', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch1_P1.db
title:
an-electron-in-a-hydrogenlike-atom-is-in-an-excited-state-it-has-a-total-energy-of-34-ev-the-kinetic-energy-and-the-debroglie-wavelength-of-the-electr

slug:
an-electron-in-a-hydrogenlike-atom-is-in-an-excited-state-it-has-a-total-energy-of-34-ev-the-kinetic-energy-and-the-debroglie-wavelength-of-the-electr-88573

question:
<div class="question">An electron, in a hydrogen-like atom, is in an excited state. It has a total energy of $-3.4 \mathrm{eV}$. The kinetic energy and the de-Broglie wavelength of the electron are respectively</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$+3.4 \mathrm{eV}, 0.66 \times 10^{-9} \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$-3.4 \mathrm{eV}, 1.99 \times 10^{-9} \mathrm{~m}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2.8 \mathrm{eV}, 2.38 \times 10^{-10} \mathrm{~m}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1.1 \mathrm{eV}, 1.28 \times 10^{-9} \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$+3.4 \mathrm{eV}, 0.66 \times 10^{-9} \mathrm{~m}$</span> </div>

answer:
<div class="solution">$E_{n}=-3.4 \mathrm{eV}$<br/>The kinetic energyis equal to the magnitude of total energy in this case. $\therefore \mathrm{K.E}=+3.4 \mathrm{eV}$<br/>The de Broglie wavelength of electron<br/>$\begin{aligned} \lambda=\frac{h}{\sqrt{2 m K}} &amp;=\frac{6.64 \times 10^{-34}}{\sqrt{2 \times 9.1 \times 10^{-31} \times 3.4 \times 1.6 \times 10^{-19}}} \mathrm{eV} \\ &amp;=0.66 \times 10^{-9} \mathrm{~m} \end{aligned}$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P1.db
title:
an-electron-moves-in-a-circular-arc-of-radius-10-m-at-a-contant-speed-of-2-1-0-7-ms-1-with-its-plane-of-motion-normal-to-magnetic-flux-density-of-1-0-

slug:
an-electron-moves-in-a-circular-arc-of-radius-10-m-at-a-contant-speed-of-2-1-0-7-ms-1-with-its-plane-of-motion-normal-to-magnetic-flux-density-of-1-0-46368

question:
<div class="question">An electron moves in a circular arc of radius 10 $\mathrm{m}$ at a contant speed of $2 \times 10^{7} \mathrm{~ms}^{-1}$ with its plane of motion normal to magnetic flux density of $10^{-5} \mathrm{~T}$. What will be the value of specific charge of the electron?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \times 10^{4} \mathrm{Ckg}^{-1}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \times 10^{5} \mathrm{Ckg}^{-1}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$5 \times 10^{6} \mathrm{Ckg}^{-1}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$2 \times 10^{11} \mathrm{Ckg}^{-1}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2 \times 10^{11} \mathrm{Ckg}^{-1}$</span> </div>

answer:
<div class="solution">$\mathrm{Bqv}=\mathrm{mv}^{2} / \mathrm{r}$ or $\mathrm{q} / \mathrm{m}=\mathrm{v} / \mathrm{rB}$.</div>


tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch1_P1.db
title:
an-electron-revolves-in-a-circular-orbit-of-radius-r-with-angular-speed-the-magnetic-field-at-the-centre-of-electron-orbit-is

slug:
an-electron-revolves-in-a-circular-orbit-of-radius-r-with-angular-speed-the-magnetic-field-at-the-centre-of-electron-orbit-is-63095

question:
<div class="question">An electron revolves in a circular orbit of radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> with angular speed <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi></math>. The magnetic field at the centre of electron orbit is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>e</mi><mi>ω</mi></mrow><mrow><mi>π</mi><mi>r</mi></mrow></mfrac></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>e</mi><mi>ω</mi></mrow><mrow><mn>4</mn><mi>π</mi><mi>r</mi></mrow></mfrac></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><msup><mi>e</mi><mn>2</mn></msup><mi>ω</mi></mrow><mrow><mn>4</mn><mi>π</mi><mi>r</mi></mrow></mfrac></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>e</mi><mi>ω</mi></mrow><mrow><mn>2</mn><mi>π</mi><mi>r</mi></mrow></mfrac></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>e</mi><mi>ω</mi></mrow><mrow><mn>4</mn><mi>π</mi><mi>r</mi></mrow></mfrac></math></span> </div>

answer:
<div class="solution"><p>Magnetic field at the centre of circular loop.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>l</mi></mrow><mrow><mn>2</mn><mi>r</mi></mrow></mfrac><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mi mathvariant="normal">i</mi></mfenced></math></p><p>Period of revolution of electron, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi><mo>=</mo></math> angular velocity of electron</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mi>ω</mi></mfrac></math></p><p>where, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi><mo>=</mo></math> angular velocity of electron.</p><p>Current produced due to movement of electron,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mfrac><mi>e</mi><mi>T</mi></mfrac><mo>=</mo><mfrac><mi>e</mi><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mi>ω</mi></mfrac></mfrac><mo>=</mo><mfrac><mrow><mi>e</mi><mi>ω</mi></mrow><mrow><mn>2</mn><mi>π</mi></mrow></mfrac></math></p><p>On substituting the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math> in Eq. (i), we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfrac><msub><mi>μ</mi><mn>0</mn></msub><mrow><mn>2</mn><mi>r</mi></mrow></mfrac><mo>·</mo><mfrac><mrow><mi>e</mi><mi>ω</mi></mrow><mrow><mn>2</mn><mi>π</mi></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>B</mi><mo>=</mo><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>e</mi><mi>ω</mi></mrow><mrow><mn>4</mn><mi>π</mi><mi>r</mi></mrow></mfrac></math></p></div>


tags: ['Chemistry', 'Solid State', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P1.db
title:
an-elemental-crystal-has-a-density-of-8570-kg-m-3-the-packing-efficiency-is-068-the-closest-distance-of-approach-between-neighbouring-atom-is-286-a-wh

slug:
an-elemental-crystal-has-a-density-of-8570-kg-m-3-the-packing-efficiency-is-068-the-closest-distance-of-approach-between-neighbouring-atom-is-286-a-wh-45604

question:
<div class="question">An elemental crystal has a density of $8570 \mathrm{~kg} / \mathrm{m}^{3}$. The packing efficiency is 0.68 . The closest distance of approach between neighbouring atom is $2.86 Ãâ¦$. What is the mass of one atom approximately?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$93 \mathrm{amu}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$39 \mathrm{amu}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$63 \mathrm{amu}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$29 \mathrm{amu}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$93 \mathrm{amu}$</span> </div>

answer:
<div class="solution">The packing efficiency $=0.68$, means the given lattice is $\mathrm{BCC}$. The closest distance of approach $=2 \mathrm{r}$
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>2 r=2.86 A=a \sqrt{3} \\
<br/> <br/>\text { or a }=\frac{2 \times 2.86}{\sqrt{3}}=3.30 Ãâ¦
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>Let atomic weight of the element $=\mathrm{a}$
<br/> <br/>$$
<br/> <br/>\begin{aligned}
<br/> <br/>\therefore &amp; \frac{2 \times 9}{36 \times 10^{23} \times(3.3)^{3} \times 10^{-24}}=8.57 \\
<br/> <br/>\mathrm{a} &amp;=8.57 \times 3 \times(3.3)^{3} \times 0.1 \\
<br/> <br/>&amp;=92.39 \simeq 93 \mathrm{amu}
<br/> <br/>\end{aligned}
<br/> <br/>$$</div>


tags: ['Mathematics', 'Ellipse', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch1_P1.db
title:
an-ellipse-has-ob-as-semi-minor-axis-f-and-f-its-focii-and-the-angle-fb-f-is-a-right-angle-then-the-eccentricity-of-the-ellipse-is

slug:
an-ellipse-has-ob-as-semi-minor-axis-f-and-f-its-focii-and-the-angle-fb-f-is-a-right-angle-then-the-eccentricity-of-the-ellipse-is-71782

question:
<div class="question">An ellipse has $O B$ as semi minor axis, $F$ and $F^{\prime}$
<br/> <br/>its focii and the angle $F B F^{\prime}$ is a right angle. Then the eccentricity of the ellipse is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{1}{\sqrt{2}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{4}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{\sqrt{3}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{\sqrt{2}}$</span> </div>

answer:
<div class="solution">$\begin{aligned} &amp; \because \angle F B F^{\prime}=90^{\circ} \Rightarrow F B^{2}+F^{\prime} B^{2}=F F^{\prime 2} \\ \therefore &amp;\left(\sqrt{a^{2} e^{2}+b^{2}}\right)^{2}+\left(\sqrt{a^{2} e^{2}+b^{2}}\right)^{2}=(2 a e)^{2} \\ &amp; \Rightarrow 2\left(a^{2} e^{2}+b^{2}\right)=4 a^{2} e^{2} \Rightarrow e^{2}=\frac{b^{2}}{a^{2}} \ldots(1) \end{aligned}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/kpmTfI4BRcO0ZxYX9ntydokI-y3lZtOTZNltcLV-Ly8.original.fullsize.png"/><br/> <br/> <br/>Also, $e^{2}=1-b^{2} / a^{2}=1-e^{2}$
<br/> <br/>(By using equation (i)) $\Rightarrow 2 e^{2}=1 \Rightarrow e=\frac{1}{\sqrt{2}}$</div>


tags: ['Mathematics', 'Ellipse', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P1.db
title:
an-ellipse-has-ob-as-semi-minor-axis-f-and-f-its-focii-and-the-angle-fbf-is-a-right-angle-then-the-eccentricity-of-the-ellipse-is-1

slug:
an-ellipse-has-ob-as-semi-minor-axis-f-and-f-its-focii-and-the-angle-fbf-is-a-right-angle-then-the-eccentricity-of-the-ellipse-is-1-67412

question:
<div class="question">An ellipse has $\mathrm{OB}$ as semi minor axis, $\mathrm{F}$ and $\mathrm{F}^{\prime}$ its focii and the angle FBF' is a right angle. Then the eccentricity of the ellipse is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{1}{\sqrt{2}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{4}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{\sqrt{3}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{\sqrt{2}}$</span> </div>

answer:
<div class="solution">$\because \angle \mathrm{FBF}^{\prime}=90^{\circ}$
<br/> <br/>$\Rightarrow \mathrm{FB}^{2}+\mathrm{F}^{\prime} \mathrm{B}^{2}=\mathrm{FF}^{\prime 2}$
<br/> <br/>$\therefore\left(\sqrt{a^{2} e^{2}+b^{2}}\right)^{2}+\left(\sqrt{a^{2} e^{2}+b^{2}}\right)^{2}=(2 a e)^{2}$
<br/> <br/>$\Rightarrow 2\left(a^{2} e^{2}+b^{2}\right)=4 a^{2} e^{2}$
<br/> <br/>$\Rightarrow e^{2}=\frac{b^{2}}{a^{2}}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/qqG2CtULR4Qizjzl6dtVQNINLlZsYB1djhzAAe6QstE.original.fullsize.png"/><br/> <br/> <br/>Also $e^{2}=1-\frac{b^{2}}{a^{2}}=1-e^{2}$
<br/> <br/>$\begin{array}{l}
<br/> <br/>\Rightarrow 2 e^{2}=1 \\
<br/> <br/>\Rightarrow e=\frac{1}{\sqrt{2}}
<br/> <br/>\end{array}$</div>


title: an-equation-of-plane-parallel-to-plane-x-2-y-2-z-5-0-and-at-a-unit-distance-from-the-origin-is
tags: ['Mathematics', 'Three Dimensional Geometry', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch1_P1.db
slug:
an-equation-of-plane-parallel-to-plane-x-2-y-2-z-5-0-and-at-a-unit-distance-from-the-origin-is-15664

question:
<div class="question">An equation of plane parallel to plane <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>2</mn><mi>z</mi><mo>-</mo><mn>5</mn><mo>=</mo><mn>0</mn></math> and at a unit distance from the origin is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>2</mn><mi>z</mi><mo>=</mo><mn>3</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>2</mn><mi>z</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>0</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>2</mn><mi>z</mi><mo>-</mo><mn>1</mn><mo>=</mo><mn>0</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>2</mn><mi>z</mi><mo>+</mo><mn>5</mn><mo>=</mo><mn>0</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>2</mn><mi>z</mi><mo>=</mo><mn>3</mn></math></span> </div>

answer:
<div class="solution"><p>Equation of plane parallel to the plane </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>2</mn><mi>z</mi><mo>-</mo><mn>5</mn><mo>=</mo><mn>0</mn></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>2</mn><mi>z</mi><mo>+</mo><mi>λ</mi><mo>=</mo><mn>0</mn></math></p><p>Since, this plane is unit distance from origin</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mn>1</mn><mo>=</mo><mfenced close="|" open="|"><mfrac><mi>λ</mi><msqrt><mn>1</mn><mo>+</mo><mn>4</mn><mo>+</mo><mn>4</mn></msqrt></mfrac></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>|</mo><mi>λ</mi><mo>|</mo><mo>=</mo><mn>3</mn><mo>⇒</mo><mi>λ</mi><mo>=</mo><mo>±</mo><mn>3</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Equation of plane is</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>2</mn><mi>z</mi><mo>=</mo><mn>3</mn></math></p></div>


tags: ['Physics', 'Rotational Motion', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
an-equilateral-prism-of-mass-m-rests-on-a-rough-horizontal-surface-with-coefficient-of-friction-a-horizontal-force-f-is-applied-on-the-prism-as-shown--1

slug:
an-equilateral-prism-of-mass-m-rests-on-a-rough-horizontal-surface-with-coefficient-of-friction-a-horizontal-force-f-is-applied-on-the-prism-as-shown-1-29186

question:
<div class="question">An equilateral prism of mass $\mathrm{m}$ rests on a rough horizontal surface with coefficient of friction $\mu$. A horizontal force $\mathrm{F}$ is applied on the prism as shown in the figure. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, then the minimum force required to topple the prism is -
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/llXXsXulrOCyOdtelaS45eSo9yo_CjwnnymwqnSD6ns.original.fullsize.png"/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{\mathrm{mg}}{\sqrt{3}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\mathrm{mg}}{4}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\mu \mathrm{mg}}{\sqrt{3}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\mu \mathrm{mg}}{4}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{mg}}{\sqrt{3}}$</span> </div>

answer:
<div class="solution">The tendency of rotation will be about the point C.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/7ajHS5azpo3enZxCfEwUl-mLjm-Bs22Hrq93d634eSk.original.fullsize.png"/><br/> <br/> <br/>For minimum force, the torque of $\mathrm{F}$ about $\mathrm{C}$ has to be equal to the torque of $\mathrm{mg}$ about $\mathrm{C}$.
<br/> <br/>$$
<br/> <br/>\therefore \quad \mathrm{F}\left(\mathrm{a} \frac{\sqrt{3}}{2}\right)=\mathrm{mg}\left(\frac{\mathrm{a}}{2}\right) \Rightarrow \mathrm{F}=\frac{\mathrm{mg}}{\sqrt{3}}
<br/> <br/>$$</div>


tags: ['Physics', 'Rotational Motion', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P1.db
title:
an-equilateral-prism-of-mass-m-rests-on-a-rough-horizontal-surface-with-coefficient-of-friction-a-horizontal-force-f-is-applied-on-the-prism-as-shown-

slug:
an-equilateral-prism-of-mass-m-rests-on-a-rough-horizontal-surface-with-coefficient-of-friction-a-horizontal-force-f-is-applied-on-the-prism-as-shown-34877

question:
<div class="question">An equilateral prism of mass $\mathrm{m}$ rests on a rough horizontal surface with coefficient of friction $\mu$. A horizontal force $\mathrm{F}$ is applied on the prism as shown in the figure. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, then the minimum force required to topple the prism is -
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/llXXsXulrOCyOdtelaS45eSo9yo_CjwnnymwqnSD6ns.original.fullsize.png"/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{\mathrm{mg}}{\sqrt{3}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\mathrm{mg}}{4}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\mu \mathrm{mg}}{\sqrt{3}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\mu \mathrm{mg}}{4}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{mg}}{\sqrt{3}}$</span> </div>

answer:
<div class="solution">The tendency of rotation will be about the point C.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/7ajHS5azpo3enZxCfEwUl-mLjm-Bs22Hrq93d634eSk.original.fullsize.png"/><br/> <br/> <br/>For minimum force, the torque of $\mathrm{F}$ about $\mathrm{C}$ has to be equal to the torque of $\mathrm{mg}$ about $\mathrm{C}$.
<br/> <br/>$$
<br/> <br/>\therefore \quad \mathrm{F}\left(\mathrm{a} \frac{\sqrt{3}}{2}\right)=\mathrm{mg}\left(\frac{\mathrm{a}}{2}\right) \Rightarrow \mathrm{F}=\frac{\mathrm{mg}}{\sqrt{3}}
<br/> <br/>$$</div>


tags: ['Chemistry', 'Chemical Equilibrium', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch1_P1.db
title:
an-equilibrium-mixture-at-300-k-contains-n-2-o-4-and-no-2-at-0-28-and-1-1-atm-pressure-respectively-if-the-volume-of-the-container-is-doubled-the-new-

slug:
an-equilibrium-mixture-at-300-k-contains-n-2-o-4-and-no-2-at-0-28-and-1-1-atm-pressure-respectively-if-the-volume-of-the-container-is-doubled-the-new-72662

question:
<div class="question">An equilibrium mixture at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><mo> </mo><mi mathvariant="normal">K</mi></math> contains <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>4</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>NO</mi><mn>2</mn></msub></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>28</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>1</mn><mo> </mo><mi>atm</mi></math> pressure, respectively. If the volume of the container is doubled, the new equilibrium pressure of these two gases are respectively.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>064</mn><mo> </mo><mi>atm</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>095</mn><mo> </mo><mi>atm</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>64</mn><mo> </mo><mi>atm</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>095</mn><mo> </mo><mi>atm</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>095</mn><mo> </mo><mi>atm</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>632</mn><mo> </mo><mi>atm</mi></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>095</mn><mo> </mo><mi>atm</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>64</mn><mo> </mo><mi>atm</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>095</mn><mo> </mo><mi>atm</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>64</mn><mo> </mo><mi>atm</mi></math></span> </div>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>4</mn></msub><mfenced><mi mathvariant="normal">g</mi></mfenced><mo>⇌</mo><mn>2</mn><msub><mi>NO</mi><mn>2</mn></msub><mfenced><mi mathvariant="normal">g</mi></mfenced></math></p><p>Pressure at equilibrium<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mi mathvariant="normal">p</mi></msub><mo>=</mo><mfrac><msubsup><mi mathvariant="normal">p</mi><msub><mi>NO</mi><mn>2</mn></msub><mn>2</mn></msubsup><msub><mi mathvariant="normal">p</mi><mrow><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>4</mn></msub></mrow></msub></mfrac><mo>=</mo><mfrac><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mrow><mn>0</mn><mo>.</mo><mn>28</mn></mrow></mfrac><mo>=</mo><mn>4</mn><mo>.</mo><mn>32</mn><mo> </mo><mi>atm</mi></math></p><p>If volume of the container is doubled, the pressure will reduced to half</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>4</mn></msub><mo>⇌</mo><mn>2</mn><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi></math></p><p>New pressure,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mfrac><mrow><mn>0</mn><mo>.</mo><mn>028</mn></mrow><mn>2</mn></mfrac><mo>-</mo><mi mathvariant="normal">p</mi></mrow></mfenced><mfenced close="]" open="["><mrow><mfrac><mrow><mn>1</mn><mo>.</mo><mn>1</mn></mrow><mn>2</mn></mfrac><mo>+</mo><mn>2</mn><mi mathvariant="normal">p</mi></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mi mathvariant="normal">p</mi></msub><mo>=</mo><mfrac><msup><mfenced close="]" open="["><mrow><mfrac><mrow><mn>1</mn><mo>.</mo><mn>1</mn></mrow><mn>2</mn></mfrac><mo>+</mo><mn>2</mn><mi mathvariant="normal">p</mi></mrow></mfenced><mn>2</mn></msup><mfenced close="]" open="["><mrow><mfrac><mrow><mn>0</mn><mo>.</mo><mn>28</mn></mrow><mn>2</mn></mfrac><mo>-</mo><mi mathvariant="normal">p</mi></mrow></mfenced></mfrac><mo>=</mo><mn>4</mn><mo>.</mo><mn>32</mn></math></p><p>On solving, we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>045</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><msub><mi mathvariant="normal">p</mi><mrow><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>4</mn></msub></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>14</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>045</mn><mo>=</mo><mn>0</mn><mo>.</mo><mn>095</mn><mo> </mo><mi>atm</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">p</mi><msub><mi>NO</mi><mn>2</mn></msub></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>55</mn><mo>+</mo><mfenced><mrow><mn>2</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>045</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>64</mn><mo> </mo><mi>atm</mi></math></p></div>


title: an-extremely-hot-copper-wire-reacts-with-steam-to-give
slug: an-extremely-hot-copper-wire-reacts-with-steam-to-give-42928
question: <div class="question">An extremely hot copper wire reacts with steam to give</div>
tags: ['Chemistry', 'd and f Block Elements', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{CuO}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{Cu}_{2} \mathrm{O}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Cu}_{2} \mathrm{O}_{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{CuO}_{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Cu}_{2} \mathrm{O}$</span> </div>

answer:
<div class="solution">$\underset{\text { Hot }}{2 \mathrm{Cu}}+\underset{\text { Steam }}{\mathrm{H}_{2} \mathrm{O} \longrightarrow} \mathrm{Cu}_{2} \mathrm{O}+\mathrm{H}_{2} \uparrow$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch1_P1.db
title:
an-ice-block-floats-in-a-liquid-whose-density-is-less-than-water-a-part-of-block-is-outside-the-liquid-when-whole-of-ice-has-melted-the-liquid-level-w

slug:
an-ice-block-floats-in-a-liquid-whose-density-is-less-than-water-a-part-of-block-is-outside-the-liquid-when-whole-of-ice-has-melted-the-liquid-level-w-18226

question:
<div class="question">An ice block floats in a liquid whose density is less than water. A part of block is outside the liquid. When whole of ice has melted, the liquid level will</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">rise</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">go down</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">remain same</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">first rise then go down</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">go down</span> </div>

answer:
<div class="solution">Ice is lighter than water. When ice melts, the volume occupied by water is less than that of ice. Due to which the level of water goes down.</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P1.db
title:
an-iceberg-of-density-900-kgm-3-is-floating-in-water-of-density-1000-kgm-3-the-percentage-of-volume-of-iceberg-outside-the-water-is

slug:
an-iceberg-of-density-900-kgm-3-is-floating-in-water-of-density-1000-kgm-3-the-percentage-of-volume-of-iceberg-outside-the-water-is-41674

question:
<div class="question">An ice-berg of density <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>900</mn><mo> </mo><msup><mi>kgm</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></math> is floating in water of density <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn><mo> </mo><msup><mi>kgm</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></math>. The percentage of volume of ice-berg outside the water is </div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mo>%</mo></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>35</mn><mo> </mo><mo>%</mo></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mo>%</mo></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn><mo> </mo><mo>%</mo></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mo>%</mo></math></span> </div>

answer:
<div class="solution"><p>Let the volume of ice-berg is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> and its density is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ρ</mi></math>. If this ice-berg floats in water with volume <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>in</mi></msub></math> inside it, then </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>in</mi></msub><mi>σ</mi><mi>g</mi><mo>=</mo><mi>V</mi><mi>ρ</mi><mi>g</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo></math> density of water</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msub><mi>V</mi><mi>in</mi></msub><mo>=</mo><mfenced><mfrac><mi>ρ</mi><mi>σ</mi></mfrac></mfenced><mo>·</mo><mi>V</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msub><mi>V</mi><mi>out</mi></msub><mo>=</mo><mi>V</mi><mo>-</mo><msub><mi>V</mi><mi>in</mi></msub></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfenced close="]" open="["><mfrac><mrow><mi>σ</mi><mo>-</mo><mi>ρ</mi></mrow><mi>σ</mi></mfrac></mfenced><mo> </mo><mi>V</mi><mo>=</mo><mfrac><mrow><mn>1000</mn><mo>-</mo><mn>900</mn></mrow><mn>1000</mn></mfrac><mo> </mo><mi mathvariant="normal">V</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mi>V</mi><mn>10</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msub><mi>V</mi><mi>out</mi></msub><mo> </mo><mo>/</mo><mi>V</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>=</mo><mn>10</mn><mo> </mo><mo>%</mo></math></p></div>


tags: ['Physics', 'Thermodynamics', 'BITSAT', 'BITSAT 2021']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$1.4$</span> </div>
source_db: MarksBatch1_P1.db
title:
an-ideal-gas-at-atmospheric-pressure-is-adiabatically-compressed-so-that-its-density-becomes-32-times-of-its-initial-value-if-the-final-pressure-of-ga-1

slug:
an-ideal-gas-at-atmospheric-pressure-is-adiabatically-compressed-so-that-its-density-becomes-32-times-of-its-initial-value-if-the-final-pressure-of-ga-1-78456

question:
<div class="question">An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes 32 times of its initial value. If the final pressure of gas is 128 atmospheres, the value of ' $\gamma$ ' of the gas is :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1.5$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$1.4$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1.3$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1.6$</span> </li> </ul>

answer:
<div class="solution">Volume $v=\frac{\mathrm{m}}{d}$ and using $\mathrm{PV}^{\gamma}=$ constant
<br/> <br/>$\begin{array}{l}
<br/> <br/>\frac{\mathrm{P}^{\prime}}{\mathrm{P}}=\frac{\mathrm{V}}{\mathrm{V}^{\prime}}=\left(\frac{\mathrm{d}^{\prime}}{\mathrm{d}}\right)^{\gamma} \\
<br/> <br/>\text { or } 128=(32)^{\gamma} \\
<br/> <br/>\therefore \gamma=\frac{7}{5}=1.4
<br/> <br/>\end{array}$</div>


title: an-ideal-gas-cant-be-liquefied-because
slug: an-ideal-gas-cant-be-liquefied-because-33513
question: <div class="question">An ideal gas can't be liquefied because</div>
tags: ['Chemistry', 'States of Matter', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">its critical temperature is always above $0^{\circ} \mathrm{C}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">its molecules are relativelysmaller in size</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">it solidifies before becoming a liquid</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">forces operated between its molecules are negligible</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">forces operated between its molecules are negligible</span> </div>

answer:
<div class="solution">In an ideal gas, the intermolecular forces of attraction are negligible and hence it cannot be liquefied.</div>


tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'BITSAT', 'BITSAT 2020']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0.4</span> </div>
source_db: MarksBatch1_P1.db
title:
an-ideal-gaseous-mixture-of-ethane-c-2-h-6-and-ethene-c-2-h-4-occupies-28-litre-at-1-atm-and-273-k-the-mixture-reacts-completely-with-128-g-o-2-to-pro

slug:
an-ideal-gaseous-mixture-of-ethane-c-2-h-6-and-ethene-c-2-h-4-occupies-28-litre-at-1-atm-and-273-k-the-mixture-reacts-completely-with-128-g-o-2-to-pro-35402

question:
<div class="question">An ideal gaseous mixture of ethane $\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)$ and ethene $\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)$ occupies 28 litre at 1 atm and $273 \mathrm{~K}$. The mixture reacts completely with $128 \mathrm{~g}$ $\mathrm{O}_{2}$ to produce $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O} .$ Mole fraction at $\mathrm{C}_{2} \mathrm{H}_{6}$ in the mixture is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0.6</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">0.4</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">0.5</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">0.8</span> </li> </ul>

answer:
<div class="solution">$\mathrm{C}_{2} \mathrm{H}_{6}+3.5 \mathrm{O}_{2} \longrightarrow 2 \mathrm{CO}_{2}+3 \mathrm{H}_{2} \mathrm{O} ;$
<br/> <br/>$\mathrm{C}_{2} \mathrm{H}_{4}+3 \mathrm{O}_{2} \longrightarrow 2 \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}$
<br/> <br/>Let volume of ethane is $\mathrm{x}$ litre, $22.4 \times 4=3.5 \mathrm{x}+3(28-\mathrm{x})$
<br/> <br/>$\Rightarrow \mathrm{x}=11.2$ litre
<br/> <br/>at constant $\mathrm{T}$ and $\mathrm{P}, \mathrm{V} \propto \mathrm{n} ;$
<br/> <br/>$\Rightarrow$ Mole fraction of $\mathrm{C}_{2} \mathrm{H}_{6}$ in mixture $=\frac{11.2}{28}=0.4$</div>


tags: ['Physics', 'Thermodynamics', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch1_P1.db
title:
an-ideal-monoatomic-gas-at-300-k-expands-adiabatically-to-twice-its-volume-the-final-temperature-of-gas-is

slug:
an-ideal-monoatomic-gas-at-300-k-expands-adiabatically-to-twice-its-volume-the-final-temperature-of-gas-is-38386

question:
<div class="question">An ideal monoatomic gas at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><mo> </mo><mi mathvariant="normal">K</mi></math> expands adiabatically to twice its volume. The final temperature of gas is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><msqrt><mn>2</mn></msqrt></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><msqrt><mn>3</mn></msqrt></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mfrac><mn>2</mn><mn>3</mn></mfrac></msup></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><msup><mfenced><mn>2</mn></mfenced><mfrac><mn>2</mn><mn>3</mn></mfrac></msup></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mfrac><mn>2</mn><mn>3</mn></mfrac></msup></math></span> </div>

answer:
<div class="solution"><p>For an ideal monatomic gas, the ratio of specific heat capacity at constant pressure to specific heat capacity at constant volume is</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>γ</mi><mo>=</mo><mfrac><mn>5</mn><mn>3</mn></mfrac></math></p><p>In an adiabatic process,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><msup><mi>V</mi><mrow><mi>γ</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo></math> constant</p><p>i.e. <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>f</mi></msub><msubsup><mi>V</mi><mi>f</mi><mrow><mi>γ</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>=</mo><msub><mi>T</mi><mi>i</mi></msub><msubsup><mi>V</mi><mi>i</mi><mrow><mi>γ</mi><mo>-</mo><mn>1</mn></mrow></msubsup><mo>⇒</mo><msub><mi>T</mi><mi>f</mi></msub><mo>=</mo><msub><mi>T</mi><mi>i</mi></msub><msup><mfenced><mfrac><msub><mi>V</mi><mi>i</mi></msub><msub><mi>V</mi><mi>f</mi></msub></mfrac></mfenced><mrow><mi>γ</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo><mn>300</mn><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mrow><mfrac><mn>5</mn><mn>3</mn></mfrac><mo>-</mo><mn>1</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>300</mn><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup></math></p></div>


tags: ['Physics', 'Thermodynamics', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch1_P1.db
title:
an-ideal-refrigerator-has-a-freezer-at-a-temperature-of-1-3-c-the-coefficient-of-performance-of-the-engine-is-5-the-temperature-of-the-air-to-which-he

slug:
an-ideal-refrigerator-has-a-freezer-at-a-temperature-of-1-3-c-the-coefficient-of-performance-of-the-engine-is-5-the-temperature-of-the-air-to-which-he-53459

question:
<div class="question">An ideal refrigerator has a freezer at a temperature of $13^{\circ} \mathrm{C}$. The coefficient of performance of the engine is $5 .$ The temperature of the air (to which heat is rejected) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$320^{\circ} \mathrm{C}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$39^{\circ} \mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$325 \mathrm{~K}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$325^{\circ} \mathrm{C}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$39^{\circ} \mathrm{C}$</span> </div>

answer:
<div class="solution">$\mathrm{T}_{2}=273-13=260$,<br/>$$<br/>\mathrm{K}=\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}-\mathrm{T}_{2}} ; \quad 5=\frac{260}{\mathrm{~T}_{1}-260}<br/>$$<br/>or $\mathrm{T}_{1}-260=52 ; \quad \mathrm{T}_{1}=312 \mathrm{~K}$<br/>$\mathrm{T}_{2}=312-273=39^{\circ} \mathrm{C}$</div>


tags: ['Physics', 'Electromagnetic Induction', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
an-inductor-of-inductance-l-400-mh-and-resistors-of-resistance-r-1-2-and-r-2-2-are-connected-to-a-battery-of-emf-12-v-as-shown-in-the-figure-the-inter-1

slug:
an-inductor-of-inductance-l-400-mh-and-resistors-of-resistance-r-1-2-and-r-2-2-are-connected-to-a-battery-of-emf-12-v-as-shown-in-the-figure-the-inter-1-77924

question:
<div class="question">An inductor of inductance $L=400 \mathrm{mH}$ and resistors of resistance $R_{1}=2 \Omega$ and $R_{2}=2 \Omega$ are connected to a battery of emf $12 \mathrm{~V}$ as shown in the figure. The internal resistance of the battery is negligible. The switch $S$ is closed at $t=0 .$ The potential drop across $L$ as a function of time is
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/7X35j8e3bYNhi279A5VMee8ezq0Qbq7rDaH9QG_3jeg.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{12}{t} e^{-3 t} \mathrm{~V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$6\left(1-e^{-t / 0.2}\right) \mathrm{V}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$12 \mathrm{e}^{-5 t} \mathrm{~V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$6 \mathrm{e}^{-5 t} \mathrm{~V}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$12 \mathrm{e}^{-5 t} \mathrm{~V}$</span> </div>

answer:
<div class="solution">Growth in current in $L R_{2}$ branch when switch is closed is given by
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>i=\frac{E}{R_{2}}\left[1-e^{-R_{2} t / L}\right] \\
<br/> <br/>\Rightarrow \frac{d i}{d t}=\frac{E}{R_{2}} \cdot \frac{R_{2}}{L} e^{-R_{2} t / L}=\frac{E}{L} e^{-\frac{R_{2} t}{L}}
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>Hence, potential drop across $\mathbf{L}=\left(\frac{E}{L} e^{-R_{2} t / L}\right) L=E e^{-R_{2} t / L}$
<br/> <br/>$=12 e^{-\frac{2 t}{400 \times 10^{-3}}}=12 \mathrm{e}^{-5 t} \mathrm{~V}$</div>


tags: ['Physics', 'Electromagnetic Induction', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch1_P1.db
title:
an-inductor-of-inductance-l-400-mh-and-resistors-of-resistance-r-1-2-and-r-2-2-are-connected-to-a-battery-of-emf-12-v-as-shown-in-the-figure-the-inter

slug:
an-inductor-of-inductance-l-400-mh-and-resistors-of-resistance-r-1-2-and-r-2-2-are-connected-to-a-battery-of-emf-12-v-as-shown-in-the-figure-the-inter-31369

question:
<div class="question">An inductor of inductance $L=400 \mathrm{mH}$ and resistors of resistance $R_{1}=2 \Omega$ and $R_{2}=2 \Omega$ are connected to a battery of emf $12 \mathrm{~V}$ as shown in the figure. The internal resistance of the battery is negligible. The switch $S$ is closed at $t=0 .$ The potential drop across $L$ as a function of time is
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/7X35j8e3bYNhi279A5VMee8ezq0Qbq7rDaH9QG_3jeg.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{12}{t} e^{-3 t} \mathrm{~V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$6\left(1-e^{-t / 0.2}\right) \mathrm{V}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$12 \mathrm{e}^{-5 t} \mathrm{~V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$6 \mathrm{e}^{-5 t} \mathrm{~V}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$12 \mathrm{e}^{-5 t} \mathrm{~V}$</span> </div>

answer:
<div class="solution">Growth in current in $L R_{2}$ branch when switch is closed is given by
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>i=\frac{E}{R_{2}}\left[1-e^{-R_{2} t / L}\right] \\
<br/> <br/>\Rightarrow \frac{d i}{d t}=\frac{E}{R_{2}} \cdot \frac{R_{2}}{L} e^{-R_{2} t / L}=\frac{E}{L} e^{-\frac{R_{2} t}{L}}
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>Hence, potential drop across $\mathbf{L}=\left(\frac{E}{L} e^{-R_{2} t / L}\right) L=E e^{-R_{2} t / L}$
<br/> <br/>$=12 e^{-\frac{2 t}{400 \times 10^{-3}}}=12 \mathrm{e}^{-5 t} \mathrm{~V}$</div>


tags: ['Physics', 'Oscillations', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P1.db
title:
an-instantaneous-displacement-of-a-simple-harmonic-oscillator-is-x-a-cos-t-4-its-speed-will-be-maximum-at-time-1

slug:
an-instantaneous-displacement-of-a-simple-harmonic-oscillator-is-x-a-cos-t-4-its-speed-will-be-maximum-at-time-1-85975

question:
<div class="question">An instantaneous displacement of a simple harmonic oscillator is $x=A \cos (\omega t+\pi / 4)$. Its speed will be maximum at time</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\pi / 4 \omega$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\pi / 2 \omega$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\pi / \omega$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 \pi \omega$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\pi / 4 \omega$</span> </div>

answer:
<div class="solution">Velocity, $v=\frac{d x}{d t}=-A \omega \sin (\omega t+\pi / 4)$
<br/> <br/>Velocity will be maximum, when $\omega t+\pi / 4=\pi / 2$ or $\omega t=\pi / 2-\pi / 4=\pi / 4$ or $t=\pi / 4 \omega$</div>


tags: ['Physics', 'Oscillations', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch1_P1.db
title:
an-instantaneous-displacement-of-a-simple-harmonic-oscillator-is-x-a-cos-t-4-its-speed-will-be-maximum-at-time

slug:
an-instantaneous-displacement-of-a-simple-harmonic-oscillator-is-x-a-cos-t-4-its-speed-will-be-maximum-at-time-24037

question:
<div class="question">An instantaneous displacement of a simple harmonic oscillator is $\mathrm{x}=\mathrm{A} \cos (\omega \mathrm{t}+\pi / 4) .$ Its speed will be maximum at time</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\pi / 4 \omega$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\pi / 2 \omega$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\pi / \omega$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 \pi \omega$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\pi / 4 \omega$</span> </div>

answer:
<div class="solution">Velocity, $\mathrm{v}=\frac{\mathrm{dx}}{\mathrm{dt}}=-\mathrm{A} \omega \sin (\omega \mathrm{t}+\pi / 4)$
<br/> <br/>Velocity will be maximum, when $\omega t+\pi / 4=\pi / 2$ or $\omega t=\pi / 2-\pi / 4=\pi / 4$
<br/> <br/>or $t=\pi / 4 \omega$</div>


tags: ['Mathematics', 'Application of Derivatives', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch1_P1.db
title:
an-inverted-conical-flask-is-being-filled-with-water-at-the-rate-of-3-cm-3-sec-1-the-height-of-the-flask-is-10-cm-and-the-radius-of-the-base-is-5-cm-h

slug:
an-inverted-conical-flask-is-being-filled-with-water-at-the-rate-of-3-cm-3-sec-1-the-height-of-the-flask-is-10-cm-and-the-radius-of-the-base-is-5-cm-h-18799

question:
<div class="question">An inverted conical flask is being filled with water at the rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><msup><mi>cm</mi><mn>3</mn></msup><mo> </mo><msup><mi>sec</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>. The height of the flask is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mi>cm</mi></math> and the radius of the base is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo> </mo><mi>cm</mi></math>. How fast is the water level rising when the level is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mi>cm</mi><mo>?</mo></math></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4</mn><mn>3</mn></mfrac><mi>π</mi><mo> </mo><mi>cm</mi><mo> </mo><msup><mi>sec</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mrow><mn>4</mn><mi>π</mi></mrow></mfrac><mo> </mo><mi>cm</mi><mo> </mo><msup><mi>sec</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mn>4</mn></mfrac><mo> </mo><mi>cm</mi><mo> </mo><msup><mi>sec</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4</mn><mrow><mn>3</mn><mi>π</mi></mrow></mfrac><mo> </mo><mi>cm</mi><mo> </mo><msup><mi>sec</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mrow><mn>4</mn><mi>π</mi></mrow></mfrac><mo> </mo><mi>cm</mi><mo> </mo><msup><mi>sec</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </div>

answer:
<div class="solution"><p>Let depth of water at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> be <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> and the radius of the base of water level be <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/5d86d575-45f8-404b-9b22-ae93feacf861-d51.png" style="width: 277px; height: 250px;"/></p><p>From similar <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>O</mi><mi>M</mi><mi>P</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>O</mi><mi>N</mi><mi>Q</mi></math>, we have</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>O</mi><mi>M</mi></mrow><mrow><mi>O</mi><mi>N</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>P</mi><mi>M</mi></mrow><mrow><mi>Q</mi><mi>N</mi></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mi>h</mi><mn>10</mn></mfrac><mo>=</mo><mfrac><mi>r</mi><mn>5</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>r</mi><mo>=</mo><mfrac><mrow><mn>5</mn><mi>h</mi></mrow><mn>10</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>r</mi><mo>=</mo><mfrac><mi>h</mi><mn>2</mn></mfrac></math></p><p>We have, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>π</mi><msup><mi>r</mi><mn>2</mn></msup><mi>h</mi><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>π</mi><msup><mfenced><mfrac><mi>h</mi><mn>2</mn></mfrac></mfenced><mn>2</mn></msup><mi>h</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>V</mi><mo>=</mo><mfrac><mrow><mi>π</mi><msup><mi>h</mi><mn>3</mn></msup></mrow><mn>12</mn></mfrac></math></p><p>On differentiating both sides, we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>d</mi><mi>V</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mi>π</mi><mn>12</mn></mfrac><mo>·</mo><mn>3</mn><msup><mi>h</mi><mn>2</mn></msup><mfrac><mrow><mi>d</mi><mi>h</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>π</mi><msup><mi>h</mi><mn>2</mn></msup></mrow><mn>4</mn></mfrac><mfrac><mrow><mi>d</mi><mi>h</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></math></p><p>Given, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>d</mi><mi>V</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mn>3</mn><mo> </mo><msup><mi>cm</mi><mn>3</mn></msup><mo> </mo><msup><mi>sec</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>4</mn><mo> </mo><mi>cm</mi><mo>,</mo></math> so we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>=</mo><mfrac><mrow><mi>π</mi><mo>×</mo><msup><mn>4</mn><mn>2</mn></msup></mrow><mn>4</mn></mfrac><mfrac><mrow><mi>d</mi><mi>h</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mrow><mi>d</mi><mi>h</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mn>3</mn><mrow><mn>4</mn><mi>π</mi></mrow></mfrac><mo> </mo><mi>cm</mi><mo> </mo><msup><mi>sec</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p><p>Hence, the water level is rising at <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mrow><mn>4</mn><mi>π</mi></mrow></mfrac><mo> </mo><mi>cm</mi><mo> </mo><msup><mi>sec</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Option (b) is correct.</p></div>


tags: ['Physics', 'Mechanical Properties of Solids', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch1_P1.db
title:
an-iron-rod-of-length-2-m-and-crosssectional-area-of-50-mm-2-stretched-by-05-mm-when-a-mass-of-250-kg-is-hung-from-its-lower-end-youngs-modulus-of-iro

slug:
an-iron-rod-of-length-2-m-and-crosssectional-area-of-50-mm-2-stretched-by-05-mm-when-a-mass-of-250-kg-is-hung-from-its-lower-end-youngs-modulus-of-iro-71465

question:
<div class="question">An iron rod of length $2 \mathrm{~m}$ and cross-sectional area of $50 \mathrm{~mm}^{2}$ stretched by $0.5 \mathrm{~mm}$, when a mass of $250 \mathrm{~kg}$ is hung from its lower end. Young's modulus of iron rod is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$19.6 \times 10^{20} \mathrm{~N} / \mathrm{m}^{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$19.6 \times 10^{18} \mathrm{~N} / \mathrm{m}^{2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$19.6 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$19.6 \times 10^{15} \mathrm{~N} / \mathrm{m}^{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$19.6 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$</span> </div>

answer:
<div class="solution">$Y=\frac{\mathrm{F} / \mathrm{A}}{\Delta \ell / \ell}=\frac{\frac{250 \times 9.8}{50 \times 10^{-6}}}{\frac{0.5 \times 10^{-3}}{2}}$<br/>$=\frac{250 \times 9.8}{50 \times 10^{-6}} \times \frac{2}{0.5 \times 10^{-3}} \Rightarrow 19.6 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$</div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch1_P1.db
title:
an-object-experiences-a-net-force-and-accelerates-from-rest-to-its-final-position-in-16-s-how-long-would-the-object-take-to-reach-the-same-final-posit

slug:
an-object-experiences-a-net-force-and-accelerates-from-rest-to-its-final-position-in-16-s-how-long-would-the-object-take-to-reach-the-same-final-posit-89237

question:
<div class="question">An object experiences a net force and accelerates from rest to its final position in $16 \mathrm{~s}$. How long would the object take to reach the same final position from rest if the object's mass was four times larger ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$64 \mathrm{~s}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$32 \mathrm{~s}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$16 \mathrm{~s}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$8 \mathrm{~s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$32 \mathrm{~s}$</span> </div>

answer:
<div class="solution">When the mass increases by a factor of 4 the acceleration must decrease by a factor of four if the same force is applied. The question asks about position so we need to relate acceleration and time to position. We can do this by the equation $: x_{f}-x_{i}=v_{x i} t+1 / 2 a_{x} t^{2}$ We want the change in position to stay the same. The initial velocity is zero so in order for the change in position to remain constant the term $(1 / 2)$ at $^{2}$ must remain the same. If the acceleration is reduced by a factor of 4 you can see that the time must be increased by a factor of 2 in order for the term to remain the same.</div>


tags: ['Mathematics', 'Trigonometric Equations', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
an-object-is-obseved-from-the-points-a-b-and-c-lying-in-a-horizontal-straight-line-which-passes-directly-underneath-the-object-the-angular-elevation-a-1

slug:
an-object-is-obseved-from-the-points-a-b-and-c-lying-in-a-horizontal-straight-line-which-passes-directly-underneath-the-object-the-angular-elevation-a-1-47663

question:
<div class="question">An object is obseved from the points $A, B$ and C lying in a horizontal straight line which passes directly underneath the object. The angular elevation at $\mathrm{B}$ is twice that at $\mathrm{A}$ and at $\mathrm{C}$ three times that at $\mathrm{A} .$ It $\mathrm{AB}=a, \mathrm{BC}=b$, then the height of the object is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{b}{2 a} \sqrt{(a+b)(3 b-a)}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{a}{b} \sqrt{(a+b)(3 b-a)}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{\mathrm{a}}{2 \mathrm{~b}} \sqrt{(\mathrm{a}+\mathrm{b})(3 \mathrm{~b}-\mathrm{a})}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{2 a}{b} \sqrt{(a+b)(3 b-a)}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{a}}{2 \mathrm{~b}} \sqrt{(\mathrm{a}+\mathrm{b})(3 \mathrm{~b}-\mathrm{a})}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/rwdKoQrfKyk9Z0EX5JJEz95pGwrs8huU3BDOAEBcdXk.original.fullsize.png"/><br/> <br/> <br/>Let $\mathrm{ED}=h, \angle \mathrm{EAB}=\alpha$
<br/> <br/>$\therefore \quad \angle \mathrm{EBD}=2 \alpha, \angle \mathrm{ECD}=3 \alpha$
<br/> <br/>Now, $\angle \mathrm{DBE}=\angle \mathrm{EAB}+\angle \mathrm{BEA}$
<br/> <br/>$\Rightarrow \quad 2 \alpha=\alpha+\angle \mathrm{BEA}$
<br/> <br/>$\Rightarrow \quad \angle \mathrm{BEA}=\alpha=\angle \mathrm{EAB}$
<br/> <br/>$\Rightarrow \mathrm{AB}=\mathrm{EB}=a$
<br/> <br/>Similarly, $\angle \mathrm{EBC}=\alpha$ $\operatorname{In} \Delta \mathrm{EBC}, \frac{\mathrm{BC}}{\sin \alpha}=\frac{\mathrm{EB}}{\sin \left(180^{\circ}-3 \alpha\right)}$
<br/> <br/>$\Rightarrow \frac{b}{\sin \alpha}=\frac{a}{\sin 3 \alpha} \Rightarrow \frac{a}{b}=\frac{\sin 3 \alpha}{\sin 3 \alpha}$
<br/> <br/>$\Rightarrow \quad \frac{a}{b}=\frac{3 \sin \alpha-4 \sin ^{3} \alpha}{\sin \alpha}=3-4 \sin ^{2} \alpha$
<br/> <br/>$\Rightarrow 4 \sin ^{2} \alpha=3-\frac{a}{b}=\frac{3 b-a}{b}$
<br/> <br/>$\Rightarrow \sin \alpha=\sqrt{\frac{3 b-a}{4 b}}$
<br/> <br/>In $\Delta \mathrm{EBD}, \sin 2 \alpha=\frac{E D}{E B}$
<br/> <br/>$\Rightarrow \quad \mathrm{ED}=\mathrm{a} \cdot 2 \sin \alpha \cdot \cos \alpha$
<br/> <br/>$\Rightarrow h=2 a \sqrt{\frac{3 b-a}{4 b}}, \sqrt{1-\frac{3 b-a}{4 b}}$
<br/> <br/>$=2 a \sqrt{\frac{3 b-a}{4 b}} \sqrt{\frac{b-a}{4 b}}$
<br/> <br/>$=\frac{a}{2 b} \sqrt{(a+b)(3 b-a)}$</div>


tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch1_P1.db
title:
an-object-is-obseved-from-the-points-a-b-and-c-lying-in-a-horizontal-straight-line-which-passes-directly-underneath-the-object-the-angular-elevation-a

slug:
an-object-is-obseved-from-the-points-a-b-and-c-lying-in-a-horizontal-straight-line-which-passes-directly-underneath-the-object-the-angular-elevation-a-93428

question:
<div class="question">An object is obseved from the points $A, B$ and C lying in a horizontal straight line which passes directly underneath the object. The angular elevation at $\mathrm{B}$ is twice that at $\mathrm{A}$ and at $\mathrm{C}$ three times that at $\mathrm{A} .$ It $\mathrm{AB}=a, \mathrm{BC}=b$, then the height of the object is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{b}{2 a} \sqrt{(a+b)(3 b-a)}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{a}{b} \sqrt{(a+b)(3 b-a)}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{\mathrm{a}}{2 \mathrm{~b}} \sqrt{(\mathrm{a}+\mathrm{b})(3 \mathrm{~b}-\mathrm{a})}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{2 a}{b} \sqrt{(a+b)(3 b-a)}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{a}}{2 \mathrm{~b}} \sqrt{(\mathrm{a}+\mathrm{b})(3 \mathrm{~b}-\mathrm{a})}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/rwdKoQrfKyk9Z0EX5JJEz95pGwrs8huU3BDOAEBcdXk.original.fullsize.png"/><br/> <br/> <br/>Let $\mathrm{ED}=h, \angle \mathrm{EAB}=\alpha$
<br/> <br/>$\therefore \quad \angle \mathrm{EBD}=2 \alpha, \angle \mathrm{ECD}=3 \alpha$
<br/> <br/>Now, $\angle \mathrm{DBE}=\angle \mathrm{EAB}+\angle \mathrm{BEA}$
<br/> <br/>$\Rightarrow \quad 2 \alpha=\alpha+\angle \mathrm{BEA}$
<br/> <br/>$\Rightarrow \quad \angle \mathrm{BEA}=\alpha=\angle \mathrm{EAB}$
<br/> <br/>$\Rightarrow \mathrm{AB}=\mathrm{EB}=a$
<br/> <br/>Similarly, $\angle \mathrm{EBC}=\alpha$ $\operatorname{In} \Delta \mathrm{EBC}, \frac{\mathrm{BC}}{\sin \alpha}=\frac{\mathrm{EB}}{\sin \left(180^{\circ}-3 \alpha\right)}$
<br/> <br/>$\Rightarrow \frac{b}{\sin \alpha}=\frac{a}{\sin 3 \alpha} \Rightarrow \frac{a}{b}=\frac{\sin 3 \alpha}{\sin 3 \alpha}$
<br/> <br/>$\Rightarrow \quad \frac{a}{b}=\frac{3 \sin \alpha-4 \sin ^{3} \alpha}{\sin \alpha}=3-4 \sin ^{2} \alpha$
<br/> <br/>$\Rightarrow 4 \sin ^{2} \alpha=3-\frac{a}{b}=\frac{3 b-a}{b}$
<br/> <br/>$\Rightarrow \sin \alpha=\sqrt{\frac{3 b-a}{4 b}}$
<br/> <br/>In $\Delta \mathrm{EBD}, \sin 2 \alpha=\frac{E D}{E B}$
<br/> <br/>$\Rightarrow \quad \mathrm{ED}=\mathrm{a} \cdot 2 \sin \alpha \cdot \cos \alpha$
<br/> <br/>$\Rightarrow h=2 a \sqrt{\frac{3 b-a}{4 b}}, \sqrt{1-\frac{3 b-a}{4 b}}$
<br/> <br/>$=2 a \sqrt{\frac{3 b-a}{4 b}} \sqrt{\frac{b-a}{4 b}}$
<br/> <br/>$=\frac{a}{2 b} \sqrt{(a+b)(3 b-a)}$</div>


tags: ['Physics', 'Motion In One Dimension', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch1_P1.db
title:
an-object-moves-with-speed-v-1-v-2-and-v-3-along-a-line-segment-a-b-bc-and-c-d-respectively-as-shown-in-figure-where-a-b-bc-and-a-d-3-a-b-then-average

slug:
an-object-moves-with-speed-v-1-v-2-and-v-3-along-a-line-segment-a-b-bc-and-c-d-respectively-as-shown-in-figure-where-a-b-bc-and-a-d-3-a-b-then-average-42673

question:
<div class="question">An object moves with speed $v_1, v_2$ and $v_3$ along a line segment $A B, B C$ and $C D$ respectively as shown in figure. Where $A B=B C$ and $A D=3 A B$, then average speed of the object will be:<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/_0HaGMo78di3prbwk2wmHmioxKdmfhVWHtLgzdIcEj0.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{v_1 v_2 v_3}{3\left(v_1 v_2+v_2 v_3+v_3 v_1\right)}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{3 v_1 v_2 v_3}{\left(v_1 v_2+v_2 v_3+v_3 v_1\right)}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\left(u_1+z_2+v_3\right)}{3}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\left(v_1+v_2+v_3\right)}{3 v_1 v_2 v_3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{3 v_1 v_2 v_3}{\left(v_1 v_2+v_2 v_3+v_3 v_1\right)}$</span> </div>

answer:
<div class="solution">Consider,<br/>$\mathrm{AB}=x$<br/>$\mathrm{BC}=x$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/EbqEENaTNsqrjlTiWsxn2gJmzuooLaDquP4T5PeIBPI.original.fullsize.png"/><br/><br/>$2 x+\mathrm{CD}=3 x \Rightarrow \mathrm{CD}=3 x-2 x=x$<br/>Average speed of the object $ &lt; \mathrm{v}&gt;$<br/>$=\frac{\text { Total distance }}{\text { Total time }}$<br/>$ &lt; \mathrm{v}&gt;=\frac{3 x}{\frac{x}{v_1}+\frac{x}{v_2}+\frac{x}{v_3}}=\frac{3 v_1 v_2 v_3}{v_2 v_3+v_1 v_3+v_1 v_2}$</div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch1_P1.db
title:
an-object-of-mass-5-kg-is-projected-with-a-velocity-20-m-s-1-at-an-angle-60-to-the-horizontal-at-the-highest-point-of-its-path-the-projectile-explodes

slug:
an-object-of-mass-5-kg-is-projected-with-a-velocity-20-m-s-1-at-an-angle-60-to-the-horizontal-at-the-highest-point-of-its-path-the-projectile-explodes-62001

question:
<div class="question">An object of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo> </mo><mi>kg</mi></math> is projected with a velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> at an angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo>°</mo></math>, to the horizontal. At the highest point of its path, the projectile explodes and breaks up into two fragments of masses <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi>kg</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mi>kg</mi><mo>.</mo></math> The fragments separate horizontally after the explosion, which releases internal energy such that the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi><mi>E</mi></math> of the system af the highest point is doubled. The separation between the two fragments when they reach the ground is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>52</mn><mo>.</mo><mn>25</mn><mo> </mo><mi mathvariant="normal">m</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>44</mn><mo>.</mo><mn>25</mn><mo> </mo><mi mathvariant="normal">m</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>65</mn><mo>.</mo><mn>32</mn><mo> </mo><mi mathvariant="normal">m</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>78</mn><mo>.</mo><mn>76</mn><mo> </mo><mi mathvariant="normal">m</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>44</mn><mo>.</mo><mn>25</mn><mo> </mo><mi mathvariant="normal">m</mi></math></span> </div>

answer:
<div class="solution"><p>Given, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>5</mn><mo> </mo><mi>kg</mi><mo>,</mo><mi>v</mi><mo>=</mo><mn>20</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><mi>θ</mi><mo>=</mo><mn>60</mn><mo>°</mo></math></p><p>Vertical component of velocity, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>y</mi></msub><mo>=</mo><mi>v</mi><mo> </mo><mi>sin</mi><mo> </mo><mn>60</mn><mo>°</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>20</mn><mo>×</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac><mo>=</mo><mn>10</mn><msqrt><mn>3</mn></msqrt><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p><p>Time taken to reach the highest point <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math> Time taken to reach the ground from highest point.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mrow><mi>v</mi><mo> </mo><mi>sin</mi><mo> </mo><mi>θ</mi></mrow><mi>g</mi></mfrac><mo>=</mo><mfrac><msub><mi>v</mi><mi>y</mi></msub><mi>g</mi></mfrac><mo>=</mo><mfrac><mrow><mn>10</mn><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>9</mn><mo>.</mo><mn>8</mn></mrow></mfrac><mo>=</mo><mn>1</mn><mo>.</mo><mn>77</mn><mo> </mo><mi mathvariant="normal">s</mi></math></p><p>At the highest point, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> splits up into two parts of masses <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>m</mi><mn>1</mn></msub><mo>=</mo><mn>1</mn><mo> </mo><mi>kg</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>m</mi><mn>2</mn></msub><mo>=</mo><mn>4</mn><mo> </mo><mi>kg</mi></math></p><p>If their velocities are <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>1</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> respectively, then applying the principle of conservation of linear momentum, we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>m</mi><mn>1</mn></msub><msub><mi>v</mi><mn>1</mn></msub><mo>+</mo><msub><mi>m</mi><mn>2</mn></msub><msub><mi>v</mi><mn>2</mn></msub><mo>=</mo><mi>m</mi><mi>v</mi><mo> </mo><mi>cos</mi><mo> </mo><mi>θ</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>1</mn></msub><mo>+</mo><mn>4</mn><msub><mi>v</mi><mn>2</mn></msub><mo>=</mo><mn>5</mn><mo>×</mo><mn>20</mn><mo>×</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>  </mo><mfenced close="]" open="["><mrow><mo>∵</mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mi>θ</mi><mo>=</mo><mn>60</mn><mo>°</mo></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>1</mn></msub><mo>+</mo><mn>4</mn><msub><mi>v</mi><mn>2</mn></msub><mo>=</mo><mn>5</mn><mo>×</mo><mn>10</mn><mo>=</mo><mn>50</mn><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mi mathvariant="normal">i</mi></mfenced></math></p><p>Initial <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi><mi>E</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo> </mo><mi>m</mi><mo> </mo><msup><mfenced><mrow><mi>v</mi><mo> </mo><mi>cos</mi><mo> </mo><mi>θ</mi></mrow></mfenced><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>5</mn><mo>×</mo><msup><mfenced><mn>10</mn></mfenced><mn>2</mn></msup><mo>=</mo><mn>250</mn><mo> </mo><mi mathvariant="normal">J</mi></math></p><p>Final <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi><mi>E</mi><mo>=</mo><mn>2</mn></math> (initial <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi><mi>E</mi></math>)<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mo>×</mo><mn>250</mn><mo>=</mo><mn>500</mn><mo> </mo><mi mathvariant="normal">J</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo>  </mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msub><mi>m</mi><mn>1</mn></msub><msubsup><mi>v</mi><mn>1</mn><mn>2</mn></msubsup><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msub><mi>m</mi><mn>2</mn></msub><msubsup><mi>v</mi><mn>2</mn><mn>2</mn></msubsup><mo>=</mo><mn>500</mn></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>  </mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>1</mn><mo>×</mo><msubsup><mi>v</mi><mn>1</mn><mn>2</mn></msubsup><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>4</mn><mo>×</mo><msubsup><mi>v</mi><mn>2</mn><mn>2</mn></msubsup><mo>=</mo><mn>500</mn></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>  </mo><msubsup><mi>v</mi><mn>1</mn><mn>2</mn></msubsup><mo>+</mo><mn>4</mn><msubsup><mi>v</mi><mn>2</mn><mn>2</mn></msubsup><mo>=</mo><mn>1000</mn><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mi>ii</mi></mfenced></math></p><p>Solving Eq. (i) and (ii), we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>1</mn></msub><mo>=</mo><mn>30</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><mo> </mo><msub><mi>v</mi><mn>2</mn></msub><mo>=</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p><p>Hence, the separation between the two fragments</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfenced><mrow><msub><mi>v</mi><mn>1</mn></msub><mo>-</mo><msub><mi>v</mi><mn>2</mn></msub></mrow></mfenced><mo>×</mo><mi>t</mi><mo>=</mo><mfenced><mrow><mn>30</mn><mo>-</mo><mn>5</mn></mrow></mfenced><mo>×</mo><mn>1</mn><mo>.</mo><mn>77</mn><mo> </mo><mi mathvariant="normal">m</mi><mo>=</mo><mn>44</mn><mo>.</mo><mn>25</mn><mo> </mo><mi mathvariant="normal">m</mi></math></p></div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch1_P1.db
title:
an-object-takes-n-times-as-much-time-to-slide-down-a-45-rough-inclined-plane-as-it-takes-to-slide-down-a-perfectly-smooth-45-inclined-plane-the-coeffi

slug:
an-object-takes-n-times-as-much-time-to-slide-down-a-45-rough-inclined-plane-as-it-takes-to-slide-down-a-perfectly-smooth-45-inclined-plane-the-coeffi-73287

question:
<div class="question">An object takes <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> times as much time to slide down a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo>°</mo></math> rough inclined plane as it takes to slide down a perfectly smooth <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo>°</mo></math> inclined plane. The coefficient of kinetic friction between the rough plane and the object is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo><mfrac><mn>1</mn><msup><mi>n</mi><mn>2</mn></msup></mfrac></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><msup><mi>n</mi><mn>2</mn></msup></mfrac></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo><mfrac><mn>1</mn><msup><mi>n</mi><mn>2</mn></msup></mfrac></math></span> </div>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>u</mi><mi>t</mi><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>a</mi><msup><mi>t</mi><mn>2</mn></msup><mo>,</mo><mi>a</mi><mo>=</mo><mi>g</mi><mi>sin</mi><mi>θ</mi><mo>,</mo><mi>u</mi><mo>=</mo><mn>0</mn></math></p><p>Then, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>  </mo><mi>s</mi><mo>=</mo><mn>0</mn><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>a</mi><msup><mi>t</mi><mn>2</mn></msup></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mi>t</mi><mo>=</mo><msqrt><mfrac><mrow><mn>2</mn><mi>s</mi></mrow><mi>a</mi></mfrac></msqrt><mo>=</mo><msqrt><mfrac><mrow><mn>2</mn><mi>s</mi></mrow><mrow><mi>g</mi><mi>sin</mi><mi>θ</mi></mrow></mfrac></msqrt></math> [for smooth plane]</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/c266eeb4-21b6-400e-80d8-4917e55496d4-image.png" style="width: 300px; height: 181px;"/></p><p>For the rough plane. the effective value of acceleration along the incline is<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>a</mi><mo>'</mo></msup><mo>=</mo><mi>g</mi><mi>sin</mi><mi>θ</mi><mo>-</mo><msub><mi>μ</mi><mi>k</mi></msub><mi>g</mi><mi>cos</mi><mi>θ</mi></math></p><p>and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>t</mi><mo>'</mo></msup><mo>=</mo><msqrt><mfrac><mrow><mn>2</mn><mi>s</mi></mrow><mi>a</mi></mfrac></msqrt><mo>=</mo><msqrt><mfrac><mrow><mn>2</mn><mi>s</mi></mrow><mrow><mi>g</mi><mi>sin</mi><mi>θ</mi><mo>-</mo><msub><mi>μ</mi><mi>k</mi></msub><mi>g</mi><mi>cos</mi><mi>θ</mi></mrow></mfrac></msqrt></math></p><p>Now, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>  </mo><mfrac><msup><mi>t</mi><mo>'</mo></msup><mi>t</mi></mfrac><mo>=</mo><mi>n</mi><mo>=</mo><msqrt><mfrac><mrow><mi>g</mi><mi>sin</mi><mi>θ</mi></mrow><mrow><mi>g</mi><mi>sin</mi><mi>θ</mi><mo>-</mo><msub><mi>μ</mi><mi>k</mi></msub><mi>g</mi><mi>cos</mi><mi>θ</mi></mrow></mfrac></msqrt></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msqrt><mfrac><mrow><mi>sin</mi><mn>45</mn><mo>°</mo></mrow><mrow><mi>sin</mi><mn>45</mn><mo>°</mo><mo>-</mo><msub><mi>μ</mi><mi>k</mi></msub><mi>cos</mi><mn>45</mn><mo>°</mo></mrow></mfrac></msqrt></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msqrt><mfrac><mn>1</mn><mrow><mn>1</mn><mo>-</mo><msub><mi>μ</mi><mi>k</mi></msub></mrow></mfrac></msqrt></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mfrac><mn>1</mn><msup><mi>n</mi><mn>2</mn></msup></mfrac><mo>=</mo><mn>1</mn><mo>-</mo><msub><mi>μ</mi><mi>k</mi></msub><mo>⇒</mo><msub><mi>μ</mi><mi>k</mi></msub><mo>=</mo><mn>1</mn><mo>-</mo><mfrac><mn>1</mn><msup><mi>n</mi><mn>2</mn></msup></mfrac></math></p></div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
an-organ-pipe-open-from-both-end-produces-5-beats-per-second-when-vibrated-with-a-source-of-frequency-200-hz-the-second-harmonic-of-the-same-pipes-pro-1

slug:
an-organ-pipe-open-from-both-end-produces-5-beats-per-second-when-vibrated-with-a-source-of-frequency-200-hz-the-second-harmonic-of-the-same-pipes-pro-1-14856

question:
<div class="question">An organ pipe, open from both end produces 5 beats per second when vibrated with a source of frequency $200 \mathrm{~Hz}$. The second harmonic of the same pipes produces 10 beats per second with a source of frequency $420 \mathrm{~Hz}$. The fundamental frequency of organ pipe is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$195 \mathrm{~Hz}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$205 \mathrm{~Hz}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$190 \mathrm{~Hz}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$210 \mathrm{~Hz}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$205 \mathrm{~Hz}$</span> </div>

answer:
<div class="solution">Let the fundamental frequency of organ pipe be $\mathrm{f}$
<br/> <br/>Case I : $f=200 \pm 5=205 \mathrm{~Hz}$ or $195 \mathrm{~Hz}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ywxbrQVTdljHnpHBtHliQoE44rRoET_t4pqq9g_iL5g.original.fullsize.png"/><br/> <br/> <br/>Case II : frequency of 2 nd harmonic of organ pipe $=2 \mathrm{f}$ (as is clear from the second figure) $2 \mathrm{f}=420 \pm 10$ or $\mathrm{f}=210 \pm 5$ or $\mathrm{f}=205$ or 215
<br/> <br/>Hence fundamental frequency oforgan pipe $=205 \mathrm{~Hz}$</div>


tags: ['Physics', 'Waves and Sound', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P1.db
title:
an-organ-pipe-open-from-both-end-produces-5-beats-per-second-when-vibrated-with-a-source-of-frequency-200-hz-the-second-harmonic-of-the-same-pipes-pro

slug:
an-organ-pipe-open-from-both-end-produces-5-beats-per-second-when-vibrated-with-a-source-of-frequency-200-hz-the-second-harmonic-of-the-same-pipes-pro-97268

question:
<div class="question">An organ pipe, open from both end produces 5 beats per second when vibrated with a source of frequency $200 \mathrm{~Hz}$. The second harmonic of the same pipes produces 10 beats per second with a source of frequency $420 \mathrm{~Hz}$. The fundamental frequency of organ pipe is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$195 \mathrm{~Hz}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$205 \mathrm{~Hz}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$190 \mathrm{~Hz}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$210 \mathrm{~Hz}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$205 \mathrm{~Hz}$</span> </div>

answer:
<div class="solution">Let the fundamental frequency of organ pipe be $\mathrm{f}$
<br/> <br/>Case I : $f=200 \pm 5=205 \mathrm{~Hz}$ or $195 \mathrm{~Hz}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ywxbrQVTdljHnpHBtHliQoE44rRoET_t4pqq9g_iL5g.original.fullsize.png"/><br/> <br/> <br/>Case II : frequency of 2 nd harmonic of organ pipe $=2 \mathrm{f}$ (as is clear from the second figure) $2 \mathrm{f}=420 \pm 10$ or $\mathrm{f}=210 \pm 5$ or $\mathrm{f}=205$ or 215
<br/> <br/>Hence fundamental frequency oforgan pipe $=205 \mathrm{~Hz}$</div>


tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
an-organic-compound-a-c-4-h-9-cl-on-reaction-with-nadiethyl-ether-gives-a-hydrocarbon-which-on-monochlorination-gives-only-one-chloro-derivative-then--1

slug:
an-organic-compound-a-c-4-h-9-cl-on-reaction-with-nadiethyl-ether-gives-a-hydrocarbon-which-on-monochlorination-gives-only-one-chloro-derivative-then-1-24990

question:
<div class="question">An organic compound $\mathrm{A}\left(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Cl}\right)$ on reaction with Na/diethyl ether gives a hydrocarbon which on monochlorination gives only one chloro derivative, then A is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">tert-butyl chloride</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">sec-butyl chloride</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">isobutyl chloride</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{n}$ -butyl chloride</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">tert-butyl chloride</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ubHmnNcH48Axg6nHHd3O2mt2U1QX1LBljAVvRzLUlNY.original.fullsize.png"/></div>


tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P1.db
title:
an-organic-compound-a-c-4-h-9-cl-on-reaction-with-nadiethyl-ether-gives-a-hydrocarbon-which-on-monochlorination-gives-only-one-chloro-derivative-then-

slug:
an-organic-compound-a-c-4-h-9-cl-on-reaction-with-nadiethyl-ether-gives-a-hydrocarbon-which-on-monochlorination-gives-only-one-chloro-derivative-then-49462

question:
<div class="question">An organic compound $\mathrm{A}\left(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Cl}\right)$ on reaction with Na/diethyl ether gives a hydrocarbon which on monochlorination gives only one chloro derivative, then A is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">tert-butyl chloride</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">sec-butyl chloride</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">isobutyl chloride</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{n}$ -butyl chloride</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">tert-butyl chloride</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ubHmnNcH48Axg6nHHd3O2mt2U1QX1LBljAVvRzLUlNY.original.fullsize.png"/></div>


tags: ['Chemistry', 'Biomolecules', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P1.db
title:
an-organic-compound-with-the-formula-c-6-h-12-o-6-forms-a-yellow-crystalline-solid-with-phenylhydrazine-and-gives-a-mixture-of-sorbitol-and-mannitol-w

slug:
an-organic-compound-with-the-formula-c-6-h-12-o-6-forms-a-yellow-crystalline-solid-with-phenylhydrazine-and-gives-a-mixture-of-sorbitol-and-mannitol-w-42858

question:
<div class="question">An organic compound with the formula $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$ forms a yellow crystalline solid with phenylhydrazine and gives a mixture of sorbitol and mannitol when reduced with sodium. Which among the following could be the compound?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">fructose</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">glucose</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">mannose</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">sucrose</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">fructose</span> </div>

answer:
<div class="solution">Since the compound forms a yellow crystalline solid, i.e. osazone with phenylhydrazine, it may be an aldohexose or a ketohexose. Further, since on reduction, compound forms a mixture of sorbitol and mannitol, it must be a ketohexose, i.e. fructose. Recall that glucose on reduction gives only one alcohol glucitol (Sorbitol)</div>


title: an-oscillator-is-nothing-but-an-amplifer-with
slug: an-oscillator-is-nothing-but-an-amplifer-with-25676
question: <div class="question">An oscillator is nothing but an amplifer with</div>
tags: ['Physics', 'Semiconductors', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">positive feedback</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">negative feedback</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">large gain</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">no feedback</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">positive feedback</span> </div>

answer:
<div class="solution">A positive feedback from output to input in an amplifier provides oscillations of constant amplitude.</div>


tags: ['Physics', 'Atomic Physics', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P1.db
title:
an-particle-after-passing-through-potential-difference-of-v-volt-collides-with-a-nucleus-if-the-atomic-number-of-the-nucleus-is-z-then-distance-of-clo

slug:
an-particle-after-passing-through-potential-difference-of-v-volt-collides-with-a-nucleus-if-the-atomic-number-of-the-nucleus-is-z-then-distance-of-clo-15537

question:
<div class="question">An <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math>-particle after passing through potential difference of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> volt collides with a nucleus. If the atomic number of the nucleus is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z</mi></math>, then distance of closest approach is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>.</mo><mn>4</mn><mfrac><mi>Z</mi><mi>V</mi></mfrac><mo> </mo><mo>Å</mo></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>.</mo><mn>4</mn><mfrac><mi>Z</mi><mi>V</mi></mfrac><mo> </mo><mi mathvariant="normal">m</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>.</mo><mn>4</mn><mfrac><mi>V</mi><mi>Z</mi></mfrac><mo> </mo><mi mathvariant="normal">m</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>.</mo><mn>4</mn><mfrac><mi>V</mi><mi>Z</mi></mfrac><mo> </mo><mo>Å</mo></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>.</mo><mn>4</mn><mfrac><mi>Z</mi><mi>V</mi></mfrac><mo> </mo><mo>Å</mo></math></span> </div>

answer:
<div class="solution"><p>Given <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>KE</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math>-particle <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mo> </mo><mi>eV</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mfrac><mrow><mfenced><mrow><mi>Z</mi><mi>e</mi></mrow></mfenced><mfenced><mi>e</mi></mfenced></mrow><mrow><mn>4</mn><mi>π</mi><msub><mi>ε</mi><mn>0</mn></msub><mo>·</mo><mfenced><mi>KE</mi></mfenced></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>2</mn><mi>Z</mi><mi>e</mi><mo>×</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow><mrow><mn>2</mn><mi>V</mi></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mi>r</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mo>×</mo><mi>Z</mi><mo>×</mo><mn>16</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup><mo>×</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow><mrow><mn>2</mn><mi>V</mi></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>14</mn><mo>.</mo><mn>4</mn><mo>·</mo><mfrac><mi>Z</mi><mi>V</mi></mfrac><mo> </mo><mo>Å</mo></math></p></div>


tags: ['Chemistry', 'Aldehydes and Ketones', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch1_P1.db
title:
an-unsaturated-hydrocarbon-x-gives-white-precipitate-with-tollens-reagent-if-x-is-gaseous-in-nature-the-molecular-formula-of-x-is

slug:
an-unsaturated-hydrocarbon-x-gives-white-precipitate-with-tollens-reagent-if-x-is-gaseous-in-nature-the-molecular-formula-of-x-is-44964

question:
<div class="question">An unsaturated hydrocarbon <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>'</mo><mi mathvariant="normal">X</mi><mo>'</mo></math>gives white precipitate with Tollen's reagent. If <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">X</mi></math> is gaseous in nature, the molecular formula of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">X</mi></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">C</mi><mn>3</mn></msub><msub><mi mathvariant="normal">H</mi><mn>6</mn></msub></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">C</mi><mn>2</mn></msub><msub><mi mathvariant="normal">H</mi><mn>4</mn></msub></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">C</mi><mn>2</mn></msub><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">C</mi><mn>4</mn></msub><msub><mi mathvariant="normal">H</mi><mn>8</mn></msub></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">C</mi><mn>2</mn></msub><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub></math></span> </div>

answer:
<div class="solution"><p>Tollen's reagent consists of a solution of silver nitrate and ammonia.</p><p>Terminal alkynes react with tollen's reagent and form white color precipitate.</p><p>With Tollen's reagent (ammoniacal <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>AgNO</mi><mn>3</mn></msub></math>), a white precipitate of silver salt is obtained.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">H</mi><mo>-</mo><mi mathvariant="normal">C</mi><mo>≡</mo><mi mathvariant="normal">C</mi><mo>-</mo><mi mathvariant="normal">H</mi><mo>+</mo><mn>2</mn><msub><mi>AgNO</mi><mn>3</mn></msub><mo>+</mo><mn>2</mn><msub><mi>NH</mi><mn>4</mn></msub><mi>OH</mi><mo>→</mo><munder><mrow><mi>Ag</mi><mo>-</mo><mi mathvariant="normal">C</mi><mo>≡</mo><mi mathvariant="normal">C</mi><mo>-</mo><mi>Ag</mi></mrow><mrow><mi>Sliver</mi><mo> </mo><mi>acetylide</mi><mo> </mo><mo>(</mo><mi>white</mi><mo> </mo><mi>ppt</mi><mo>.</mo><mo>)</mo></mrow></munder><mo>+</mo><mn>2</mn><msub><mi>NH</mi><mn>4</mn></msub><msub><mi>NO</mi><mn>3</mn></msub><mo>+</mo><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi></math></p></div>


tags: ['Physics', 'Electromagnetic Waves', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch1_P1.db
title:
an-xray-tube-is-operated-at-15-kv-calculate-the-upper-limit-of-the-speed-of-the-electrons-striking-the-target

slug:
an-xray-tube-is-operated-at-15-kv-calculate-the-upper-limit-of-the-speed-of-the-electrons-striking-the-target-94130

question:
<div class="question">An X-ray tube is operated at $15 \mathrm{kV}$. Calculate the upper limit of the speed of the electrons striking the target.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$7.26 \times 10^{7} \mathrm{~m} / \mathrm{s}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$7.62 \times 10^{7} \mathrm{~m} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$7.62 \times 10^{7} \mathrm{~cm} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$7.26 \times 10^{9} \mathrm{~m} / \mathrm{s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$7.26 \times 10^{7} \mathrm{~m} / \mathrm{s}$</span> </div>

answer:
<div class="solution">The maximum kinetic energy of an electron accelerated through a potential difference of $\mathrm{V}$ volt is $\frac{1}{2} \mathrm{mv}^{2}=\mathrm{eV}$<br/>$$<br/>\begin{array}{l}<br/>\therefore \text { maximum velocity } \mathrm{v}=\sqrt{\frac{2 \mathrm{eV}}{\mathrm{m}}} \\<br/>\mathrm{v}=\sqrt{\frac{2 \times 1.6 \times 10^{-19} \times 15000}{9.1 \times 10^{-31}}} \\<br/>\mathrm{v}=7.26 \times 10^{7} \mathrm{~m} / \mathrm{s}<br/>\end{array}<br/>$$</div>


title: aniline-reacts-with-nitrous-acid-to-produce
slug: aniline-reacts-with-nitrous-acid-to-produce-60357
question: <div class="question">Aniline reacts with nitrous acid to produce</div>
tags: ['Chemistry', 'Amines', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">phenol</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">nitrobenzene</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">chlorobenzene</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">benzene diazonium chloride</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">benzene diazonium chloride</span> </div>

answer:
<div class="solution">When aniline is treated with nitrous acid in the presence of $\mathrm{HCl}$, then benzene diazonium chloride is obtained.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/sA5-zSN9xSSWKnD5yuRNhRQSKM92XDuwFnXAJI3G16Q.original.fullsize.png"/></div>


title: aniline-reacts-with-phosgene-and-koh-to-form
slug: aniline-reacts-with-phosgene-and-koh-to-form-18351
question: <div class="question">Aniline reacts with phosgene and $\mathrm{KOH}$ to form</div>
tags: ['Chemistry', 'Amines', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/C850GYFrfmwvQGMoHGIrBmF5nN53RLL8HcfLWfzKab4.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/peN6boTbGXanBvzmg3tZyKD7u8o-brBy7wVCGMaCBF0.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/GMytsPxpWnuwUvakN9T4r5rI9A13g1b7AFDxUJmagmA.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/tfHPc7hUR1IZbkKinqfZirSSXq0roN29M53VbSz-IDY.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/GMytsPxpWnuwUvakN9T4r5rI9A13g1b7AFDxUJmagmA.original.fullsize.png"/></span> </div>

answer:
<div class="solution">$\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}+\mathrm{COCl}_{2} \longrightarrow \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH.COCl}$</div>


title: area-bounded-by-two-branches-of-the-curve-y-x-2-x-3-and-x-1-is
slug: area-bounded-by-two-branches-of-the-curve-y-x-2-x-3-and-x-1-is-81798
tags: ['Mathematics', 'Area Under Curves', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch1_P1.db
question:
<div class="question">Area bounded by two branches of the curve <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mi>y</mi><mo>-</mo><mi>x</mi></mrow></mfenced><mn>2</mn></msup><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>4</mn></mfrac><mo> </mo><mi>sq</mi><mo> </mo><mi>unit</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>2</mn></mfrac><mo> </mo><mi>sq</mi><mo> </mo><mi>unit</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>4</mn></mfrac><mo> </mo><mi>sq</mi><mo> </mo><mi>unit</mi></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4</mn><mn>5</mn></mfrac><mo> </mo><mi>sq</mi><mo> </mo><mi>unit</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4</mn><mn>5</mn></mfrac><mo> </mo><mi>sq</mi><mo> </mo><mi>unit</mi></math></span> </div>

answer:
<div class="solution"><p>Given, curve is <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mi>y</mi><mo>-</mo><mi>x</mi></mrow></mfenced><mn>2</mn></msup><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mi>y</mi><mo>-</mo><mi>x</mi><mo>=</mo><mo>±</mo><mi>x</mi><msqrt><mi>x</mi></msqrt></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mi>y</mi><mo>=</mo><mi>x</mi><mo>±</mo><mi>x</mi><msqrt><mi>x</mi></msqrt></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/90b534b6-e3c4-4b5a-bf86-c78cbdd9038c-d43.png" style="width: 301px; height: 300px;"/></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Area bounded <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfenced close="|" open="|"><mrow><msubsup><mo>∫</mo><mn>0</mn><mn>1</mn></msubsup><mfenced close="}" open="{"><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mi>x</mi><msqrt><mi>x</mi></msqrt></mrow></mfenced><mo>-</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>x</mi><msqrt><mi>x</mi></msqrt></mrow></mfenced></mrow></mfenced><mi>d</mi><mi>x</mi></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfenced close="|" open="|"><mrow><mn>2</mn><msubsup><mo>∫</mo><mn>0</mn><mn>1</mn></msubsup><msup><mi>x</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi></mrow></mfenced><mo>=</mo><mfrac><mn>4</mn><mn>5</mn></mfrac><mo> </mo><mi>sq</mi><mo> </mo><mi>unit</mi></math></p></div>


title: area-intercepted-by-the-curves-y-cos-x-x-0-and-y-cos-2-x-x-0-is-1
slug: area-intercepted-by-the-curves-y-cos-x-x-0-and-y-cos-2-x-x-0-is-1-68291
tags: ['Mathematics', 'Area Under Curves', 'JEE Main']
source_db: MarksBatch1_P1.db
question:
<div class="question">Area intercepted by the curves $y=\cos x$ $\mathrm{x} \in[0, \pi]$ and $\mathrm{y}=\cos 2 \mathrm{x}, \mathrm{x} \in[0, \pi],$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{3 \pi}{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{3 \sqrt{3}}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{3 \pi}{4}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{3 \sqrt{3}}{4}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{3 \sqrt{3}}{4}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/zfwTWdt8ypDGn1Kd40Tfp2wMLHvDOZc5ABLKKnpg7dI.original.fullsize.png"/><br/> <br/> <br/>$$
<br/> <br/>\text { Area }=\int_{0}^{2 \pi / 3}(\cos x-\cos 2 x) d x=\frac{3 \sqrt{3}}{4}
<br/> <br/>$$</div>


title: area-of-the-circle-in-which-a-chord-of-length-2-makes-an-angle-2-at-the-centre-is-1
slug: area-of-the-circle-in-which-a-chord-of-length-2-makes-an-angle-2-at-the-centre-is-1-26865
tags: ['Mathematics', 'Circle', 'JEE Main']
source_db: MarksBatch1_P1.db
question:
<div class="question">Area of the circle in which a chord of length $\sqrt{2}$ makes an angle $\pi / 2$ at the centre, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\pi / 2$ sq units</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \pi$ sq units</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\pi$ sq units</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\pi / 4 \mathrm{sq}$ units</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\pi$ sq units</span> </div>

answer:
<div class="solution">Let $\mathrm{AB}$ be the chord of length $\sqrt{2}$. Let $\mathrm{O}$ be the centre of the circle and let $O C$ be the perpendicular from $\mathrm{O}$ on $\mathrm{AB}$.
<br/> <br/>Then $, \mathrm{AC}=\mathrm{BC}=\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}$
<br/> <br/>In $\Delta \mathrm{OBC},$ we have
<br/> <br/>$$
<br/> <br/>\begin{aligned}
<br/> <br/>\mathrm{OB} &amp;=\mathrm{BC} \operatorname{cosec} 45^{\circ} \\
<br/> <br/>&amp;=\frac{1}{\sqrt{2}} \times \sqrt{2}=1
<br/> <br/>\end{aligned}
<br/> <br/>$$
<br/> <br/>$\therefore$ Area of the circle $=\pi(\mathrm{OB})^{2}=\pi$ sq units
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/rkS101Yo4ZfgZ7sOrAb33YtaA4es0JxVX1sCGTXbd48.original.fullsize.png"/></div>


tags: ['Mathematics', 'Differential Equations', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch1_P1.db
title:
area-of-the-triangle-formed-by-the-line-xy3-and-angle-bisectors-of-the-pair-of-straight-lines-x2y22-y1-is

slug:
area-of-the-triangle-formed-by-the-line-xy3-and-angle-bisectors-of-the-pair-of-straight-lines-x2y22-y1-is-49391

question:
<div class="question">Area of the triangle formed by the line \(x+y=3\) and angle bisectors of the pair of straight lines \(x^2-y^2+2 y=1\) is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">2 sq. units</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">4 sq. units</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">6 sq. units</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">8 sq. units</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">2 sq. units</span> </div>

answer:
<div class="solution">\(\mathrm{x}^2-\mathrm{y}^2+2 \mathrm{y}=1 \Rightarrow \mathrm{x}= \pm(\mathrm{y}-1)\)<br/>Bisectors of above line are \(x=0 ~\&amp;~ y=1\)<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/q9-e-nY41f9GD5ETl-tSN4Ed4dRtdgHVdnw95PKOA4k.original.fullsize.png"/><br/><br/>So area between \(x=0, y=1 ~\&amp;~ x+y=3\) is shaded Region shown in figure.<img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/HlzbRdJnBytZmsPrh3LCzmrLogiaYjEvOdpefLciUfA.original.fullsize.png"/><br/><br/>Area \(=1 / 2 \times 2 \times 2=2\) sq. units</div>


title: arrange-the-following-ions-in-the-order-of-decreasing-x-o-bond-length-where-x-is-the-central-atom
tags: ['Chemistry', 'Classification of Elements and Periodicity in Properties', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P1.db
slug:
arrange-the-following-ions-in-the-order-of-decreasing-x-o-bond-length-where-x-is-the-central-atom-31116

question:
<div class="question">Arrange the following ions in the order of decreasing $\mathrm{X}-\mathrm{O}$ bond length, where $\mathrm{X}$ is the central atom</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{ClO}_{4}^{-}, \mathrm{SO}_{4}^{2-}, \mathrm{PO}_{4}^{3-}, \mathrm{SiO}_{4}^{-}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{SiO}_{4}^{4-}, \mathrm{PO}_{4}^{3-}, \mathrm{SO}_{4}^{2-}, \mathrm{ClO}_{4}^{-}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{SiO}_{4}^{4-}, \mathrm{PO}_{4}^{3-}, \mathrm{ClO}_{4}^{-}, \mathrm{SO}_{4}^{2-}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{SiO}_{4}^{4-}, \mathrm{SO}_{4}^{2-}, \mathrm{PO}_{4}^{3-}, \mathrm{ClO}_{4}^{-}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{SiO}_{4}^{4-}, \mathrm{PO}_{4}^{3-}, \mathrm{SO}_{4}^{2-}, \mathrm{ClO}_{4}^{-}$</span> </div>

answer:
<div class="solution">More will be the electronegativity of $\mathrm{X}$ lesser will be the bond length of $\underline{X}-\mathrm{O}$ bond.</div>


title: arsenic-containing-medicine-used-for-the-treatment-of-syphilis-is
slug: arsenic-containing-medicine-used-for-the-treatment-of-syphilis-is-83623
question: <div class="question">Arsenic containing medicine used for the treatment of syphilis, is</div>
tags: ['Chemistry', 'Chemistry in Everyday Life', 'BITSAT', 'BITSAT 2021']
answer: <div class="solution">No solution required.</div>
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">erythromycin</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">ofloxacin</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">tetracycline</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">salvarsan</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">salvarsan</span> </div>


title: aspirin-is-known-as-1
slug: aspirin-is-known-as-1-85691
question: <div class="question">Aspirin is known as :</div>
tags: ['Chemistry', 'Chemistry in Everyday Life', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">acetyl salicylic acid</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">phenyl salicylate</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">acetyl salicylate</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">methyl salicylic acid</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">acetyl salicylic acid</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/5mx9qy3jnj4pb9PWsEEGN3niVPHoQeS_nqveV6REURk.original.fullsize.png"/></div>


tags: ['Physics', 'Semiconductors', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch1_P1.db
title:
assuming-the-diodes-to-be-of-silicon-with-forward-resistance-zero-the-current-i-in-the-following-circuit-is39-assuming-the-diodes-to-be-of-silicon-wit

slug:
assuming-the-diodes-to-be-of-silicon-with-forward-resistance-zero-the-current-i-in-the-following-circuit-is39-assuming-the-diodes-to-be-of-silicon-wit-55039

question:
<div class="question">Assuming the diodes to be of silicon with forward resistance zero, the current I in the following circuit is39. Assuming the diodes to be of silicon with forward resistance zero, the current I in the following circuit is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/XLPnG4I6amaMLr-kLu1aNOJlDS9rySN38zE29q29318.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$9.65 \mathrm{~mA}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$10 \mathrm{~mA}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$10.35 \mathrm{~mA}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$10 \mathrm{~mA}$</span> </div>

answer:
<div class="solution">$I=\frac{V}{R}=\frac{20}{2 \times 10^{3}}=10 \times 10^{-3} \mathrm{~A}=10 \mathrm{~mA}$</div>


title: at-2-5-c-and-1-bar-which-of-the-following-has-a-nonzero-h-f
slug: at-2-5-c-and-1-bar-which-of-the-following-has-a-nonzero-h-f-25661
tags: ['Chemistry', 'Thermodynamics (C)', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch1_P1.db
question:
<div class="question">At $25^{\circ} \mathrm{C}$ and 1 bar which of the following has a non-zero $\Delta \mathrm{H}_{\mathrm{f}}^{\circ} ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\operatorname{Br}_{2}(\ell)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">C (graphite)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{O}_{3}(\mathrm{~g})$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{I}_{2}(\mathrm{~s})$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{O}_{3}(\mathrm{~g})$</span> </div>

answer:
<div class="solution">Ozone is allotropic form of oxygen and is of higher energy (by $68 \mathrm{~K}$ Cal mol $^{-1}$ ) than $\mathrm{O}_{2}$. Hence it can not be taken as the reference in standard state.</div>


tags: ['Chemistry', 'Electrochemistry', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P1.db
title:
at-2-5-c-the-molar-conductance-at-infinite-dilution-for-the-strong-electrolytes-naoh-nacl-and-bacl-2-are-248-1-0-4-126-1-0-4-and-280-1-0-4-sm-2-mol-1-

slug:
at-2-5-c-the-molar-conductance-at-infinite-dilution-for-the-strong-electrolytes-naoh-nacl-and-bacl-2-are-248-1-0-4-126-1-0-4-and-280-1-0-4-sm-2-mol-1-40787

question:
<div class="question">At $25^{\circ} \mathrm{C}$, the molar conductance at infinite dilution for the strong electrolytes $\mathrm{NaOH}, \mathrm{NaCl}$ and $\mathrm{BaCl}_{2}$ are $248 \times 10^{-4}, 126 \times 10^{-4}$ and $280 \times 10^{-4} \mathrm{Sm}^{2} \mathrm{~mol}^{-1}$ respectively. $\Delta_{\mathrm{m}}{ }^{0} \mathrm{Ba}(\mathrm{OH})_{2}$ in $\mathrm{Sm}^{2} \mathrm{~mol}^{-1}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$52.4 \times 10^{-4}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$524 \times 10^{-4}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$402 \times 10^{-4}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$262 \times 10^{-4}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$524 \times 10^{-4}$</span> </div>

answer:
<div class="solution">$\Delta_{\mathrm{Na}^{+}}^{\circ}+\Delta_{\mathrm{OH}^{-}}^{\circ}=248 \times 10^{-4} \mathrm{Sm}^{2} \mathrm{~mol}^{-1}$ $\Delta_{\mathrm{Na}^{+}}^{\circ}+\Delta_{\mathrm{Cl}^{-}}^{\circ}=126 \times 10^{-4} \mathrm{Sm}^{2} \mathrm{~mol}^{-1}$ $\Delta_{\mathrm{Ba}}^{\circ}{ }^{2+}+\Delta{ }_{2 \mathrm{Cl}^{-}}^{\circ}=280 \times 10^{-4} \mathrm{Sm}^{2} \mathrm{~mol}^{-1}$ $\mathrm{NoW}$, $\Delta_{\mathrm{Ba}(\mathrm{OH})_{2}}^{\circ}=\Delta_{\mathrm{BaCl}_{2}}^{\circ}+2 \Delta{ }^{\circ}{ }_{\mathrm{NaOH}}^{\circ}-2 \Delta{ }_{\mathrm{NaC} 1}^{\circ}$ $\Delta{ }_{\mathrm{Ba}(\mathrm{OH})_{2}}^{\circ}=280 \times 10^{-4}+2 \times 248 \times 10^{-4}-2 \times 126 \times 10^{-4}$ $\Delta_{\mathrm{Ba}(\mathrm{OH})_{2}}^{\circ}=524 \times 10^{-4} \mathrm{Sm}^{2} \mathrm{~mol}^{-1}$</div>


tags: ['Physics', 'Semiconductors', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch1_P2.db
title:
at-a-certain-temperature-the-number-density-of-charge-carriers-in-a-semiconductor-is-n-when-an-electric-field-is-applied-to-it-the-charge-carriers-dri

slug:
at-a-certain-temperature-the-number-density-of-charge-carriers-in-a-semiconductor-is-n-when-an-electric-field-is-applied-to-it-the-charge-carriers-dri-83117

question:
<div class="question">At a certain temperature, the number density of charge carriers in a semiconductor is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>. When an electric field is applied to it, the charge carriers drift with an average speed <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>. If the temperature of the semiconductor is raised.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> will increase but <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math> will decrease</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> will decrease but <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math> will increase</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Both <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math> will increase</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Both <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math> will decrease</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> will increase but <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math> will decrease</span> </div>

answer:
<div class="solution">On raising the temperature of the semiconductor, covalent bonds start breaking up and thus more charge carriers release. This will increase the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> and as a result the rate of collision of charge carriers will increase. This will decrease the drift speed <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>.</div>


title: at-a-constant-volume-the-specific-heat-of-a-gas-is-0075-and-its-molecular-weight-is-40-the-gas-is
tags: ['Chemistry', 'Thermodynamics (C)', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch1_P2.db
slug:
at-a-constant-volume-the-specific-heat-of-a-gas-is-0075-and-its-molecular-weight-is-40-the-gas-is-35635

question:
<div class="question">At a constant volume the specific heat of a gas is 0.075 and its molecular weight is $40 .$ The gas is:</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Monoatomic</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Diatomic</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Triatomic</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Monoatomic</span> </div>

answer:
<div class="solution">$\begin{aligned} &amp; q=\frac{c}{m} \\ &amp; \Rightarrow C_{v}=q \times m \\ &amp;=0.075 \times 40 \\ &amp;=3.0 \mathrm{cal} \\ &amp; C_{P}-C_{v}=R \\ &amp; C_{P}=C_{V}+R \\ &amp;=3+2=5 \\ &amp; \frac{C_{P}}{C_{V}}=\frac{5}{3}=1.66 \end{aligned}$<br/>Monoatomic gas</div>


title: at-an-extreme-point-of-a-function-f-x-the-tangent-to-the-curve-is-1
slug: at-an-extreme-point-of-a-function-f-x-the-tangent-to-the-curve-is-1-72190
question: <div class="question">At an extreme point of a function $f(x),$ the tangent to the curve is</div>
tags: ['Mathematics', 'Application of Derivatives', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">parallel to the $\mathrm{x}$ -axis</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">perpendicular to the $\mathrm{x}$ -axis</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">inclined at an angle $45^{\circ}$ to the $\mathrm{x}$ -axis</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">inclined at an angle $60^{\circ}$ to the $x$ -axis</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">parallel to the $\mathrm{x}$ -axis</span> </div>

answer:
<div class="solution">At an extreme point of a function $f(x)$, slope is always zero. Thus, At an extreme point of a function $f(x)$, the tangent to the curve is parallel to the x-axis.</div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch1_P2.db
title:
at-any-instant-the-velocity-of-a-particle-of-mass-500-g-is-2-t-i-3-t-2-j-ms-1-if-the-force-acting-on-the-particle-at-t-1-s-is-i-x-j-n-then-the-value-o

slug:
at-any-instant-the-velocity-of-a-particle-of-mass-500-g-is-2-t-i-3-t-2-j-ms-1-if-the-force-acting-on-the-particle-at-t-1-s-is-i-x-j-n-then-the-value-o-39032

question:
<div class="question">At any instant the velocity of a particle of mass $500 \mathrm{~g}$ is $\left(2 t \hat{i}+3 t^2 \hat{j}\right) \mathrm{ms}^{-1}$. If the force acting on the particle at $t=1 s$ is $(\hat{i}+x \hat{j}) N$. Then the value of $\mathrm{x}$ will be:</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">3</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">4</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">6</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">2</span> </li> </ul>

answer:
<div class="solution">Mass of particle, $\mathrm{m}=500 \mathrm{~g}=0.5 \mathrm{~kg}$<br/>velocity of a particle, $\vec{v}=2 t \hat{i}+3 t^2 \hat{j}$<br/>$\overrightarrow{\mathrm{a}}=\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}=2 \hat{\mathrm{i}}+6 \mathrm{t} \hat{\mathrm{j}}$<br/>at $\mathrm{t}=1, \overrightarrow{\mathrm{a}}=2 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}$<br/>Force acting on the particle,<br/>$\overrightarrow{\mathrm{F}}=\mathrm{ma}=0.5(2 \hat{\mathrm{i}}+6 \hat{\mathrm{j}})=\hat{\mathrm{i}}+3 \hat{\mathrm{j}}$<br/>$\overrightarrow{\mathrm{F}}=\hat{\mathrm{i}}+x \hat{\mathrm{j}} \quad$ Hence $x=3$</div>


